qu.env.lastSaved= Aug 15, 2005 5:06:56 PM @ qu.env.validTest= false @ qu.1.topic=12_3 Angle from a Percent@ qu.1.1.question=What angle (to the nearest degree) should be used to represent ${$p}% in a circle graph?
Do not enter the ° symbol in the answer box.@ qu.1.1.answer.num=$ans@ qu.1.1.answer.units=@ qu.1.1.showUnits=false@ qu.1.1.grading=exact_value@ qu.1.1.negStyle=minus@ qu.1.1.numStyle=thousands scientific dollars arithmetic@ qu.1.1.mode=Numeric@ qu.1.1.name=10 to 49@ qu.1.1.comment=

What angle (to the nearest degree) should be used to represent ${$p}% in a circle graph?
Do not enter the ° symbol in the answer box.

What angle is ${$p}% of 360°?
x = ${$p/100} • 360°
x = $ans°

@ qu.1.1.editing=useHTML@ qu.1.1.algorithm=$p=range(10,49,1); $ans=decimal(0,$p/100*360);@ qu.1.2.question=What angle (to the nearest degree) should be used to represent ${$p}% in a circle graph?
Do not enter the ° symbol in the answer box.@ qu.1.2.answer.num=$ans@ qu.1.2.answer.units=@ qu.1.2.showUnits=false@ qu.1.2.grading=exact_value@ qu.1.2.negStyle=minus@ qu.1.2.numStyle=thousands scientific dollars arithmetic@ qu.1.2.mode=Numeric@ qu.1.2.name=51 to 90@ qu.1.2.comment=

What angle (to the nearest degree) should be used to represent ${$p}% in a circle graph?
Do not enter the ° symbol in the answer box.

What angle is ${$p}% of 360°?
x = ${$p/100} • 360°
x = $ans°

@ qu.1.2.editing=useHTML@ qu.1.2.algorithm=$p=range(51,90,1); $ans=decimal(0,$p/100*360);@ qu.2.topic=12_3 Angle from a Ratio@ qu.2.1.question=

What angle (to the nearest degree) should be used to represent $n out of $d in a circle graph?
Do not enter the ° symbol in the answer box.

@ qu.2.1.answer.num=$ans@ qu.2.1.answer.units=@ qu.2.1.showUnits=false@ qu.2.1.grading=exact_value@ qu.2.1.negStyle=minus@ qu.2.1.numStyle=thousands scientific dollars arithmetic@ qu.2.1.mode=Numeric@ qu.2.1.name=ratio lt 50%@ qu.2.1.comment=

What angle (to the nearest degree) should be used to represent $n out of $d in a circle graph?
Do not enter the ° symbol in the answer box.

Use a proportion to find the ratio out of 360°.

360

360 • $n = $d • x
${360*$n} = ${$d}x
x = $ans°

@ qu.2.1.editing=useHTML@ qu.2.1.algorithm=$d=range(10,90,10); $n=range(2,$d/2-1,1); $ans=decimal(0,360*$n/$d);@ qu.2.2.question=

What angle (to the nearest degree) should be used to represent $n out of $d in a circle graph?
Do not enter the ° symbol in the answer box.

@ qu.2.2.answer.num=$ans@ qu.2.2.answer.units=@ qu.2.2.showUnits=false@ qu.2.2.grading=exact_value@ qu.2.2.negStyle=minus@ qu.2.2.numStyle=thousands scientific dollars arithmetic@ qu.2.2.mode=Numeric@ qu.2.2.name=ratio gt 50%@ qu.2.2.comment=

What angle (to the nearest degree) should be used to represent $n out of $d in a circle graph?
Do not enter the ° symbol in the answer box.

Use a proportion to find the ratio out of 360°.

360

360 • $n = $d • x
${360*$n} = ${$d}x
x = $ans°

@ qu.2.2.editing=useHTML@ qu.2.2.algorithm=$d=range(10,90,10); $n=range($d/2-1,$d-1,1); $ans=decimal(0,360*$n/$d);@ qu.3.topic=12_3 Angles from a Data Set@ qu.3.1.mode=Inline@ qu.3.1.name=Burger Palace@ qu.3.1.comment=

A recent survey of Burger Mania customers reported that $n1 preferred the Regular Hamburger, $n2 preferred the Cheeseburger and $n3 preferred the Deluxe Burger. You have been asked to create a circle chart for this data. Find the angle (to the nearest degree) for each category.
Do not enter the degree symbol in the answer boxes.

The total number of surveyed customers is $n1 + $n2 + $n3 = $total
Use a proportion to find the ratio out of 360°.

Hamburger

Cheeseburger

Deluxe Burger

$n1

$total

360

360 • $n1 = $total • x
${360*$n1} = ${$total}x
x = $ans1°

$n2

$total

360

360 • $n2 = $total • x
${360*$n2} = ${$total}x
x = $ans2°

$n3

$total

360

360 • $n3 = $total • x
${360*$n3} = ${$total}x
x = $ans3°

@ qu.3.1.editing=useHTML@ qu.3.1.algorithm=$n1=range(10,30,1); $n2=range(20,40,1); $n3=range(15,35,1); $total=$n1+$n2+$n3; $ans1=decimal(0,$n1/$total*360); $ans2=decimal(0,$n2/$total*360); $ans3=decimal(0,$n3/$total*360);condition:eq($ans1+$ans2+$ans3,360);@ qu.3.1.weighting=1,1,1@ qu.3.1.numbering=alpha@ qu.3.1.part.1.name=$ans1@ qu.3.1.part.1.answer.units=@ qu.3.1.part.1.numStyle=thousands scientific arithmetic@ qu.3.1.part.1.editing=useHTML@ qu.3.1.part.1.showUnits=false@ qu.3.1.part.1.question=(Unset)@ qu.3.1.part.1.mode=Numeric@ qu.3.1.part.1.grading=exact_value@ qu.3.1.part.1.negStyle=minus@ qu.3.1.part.1.answer.num=$ans1@ qu.3.1.part.2.name=$ans2@ qu.3.1.part.2.answer.units=@ qu.3.1.part.2.numStyle=thousands scientific arithmetic@ qu.3.1.part.2.editing=useHTML@ qu.3.1.part.2.showUnits=false@ qu.3.1.part.2.question=(Unset)@ qu.3.1.part.2.mode=Numeric@ qu.3.1.part.2.grading=exact_value@ qu.3.1.part.2.negStyle=minus@ qu.3.1.part.2.answer.num=$ans2@ qu.3.1.part.3.name=$ans3@ qu.3.1.part.3.answer.units=@ qu.3.1.part.3.numStyle=thousands scientific arithmetic@ qu.3.1.part.3.editing=useHTML@ qu.3.1.part.3.showUnits=false@ qu.3.1.part.3.question=(Unset)@ qu.3.1.part.3.mode=Numeric@ qu.3.1.part.3.grading=exact_value@ qu.3.1.part.3.negStyle=minus@ qu.3.1.part.3.answer.num=$ans3@ qu.3.1.question=

Hamburger <1>

Cheeseburger <2>

Deluxe Burger <3>

@ qu.3.2.mode=Inline@ qu.3.2.name=Middle School@ qu.3.2.comment=

Welkerville Middle School currently has $n1 6th grade students, $n2 7th grade students, and $n3 8th grade student. You have been asked to create a circle chart for this data. Find the angle (to the nearest degree) for each category.
Do not enter the degree symbol in the answer boxes.

The total number of students is $n1 + $n2 + $n3 = $total
Use a proportion to find the ratio out of 360°.

6th Grade

7th Grade

8th Grade

$n1

$total

360

360 • $n1 = $total • x
${360*$n1} = ${$total}x
x = $ans1°

$n2

$total

360

360 • $n2 = $total • x
${360*$n2} = ${$total}x
x = $ans2°

$n3

$total

360

360 • $n3 = $total • x
${360*$n3} = ${$total}x
x = $ans3°

@ qu.3.2.editing=useHTML@ qu.3.2.algorithm=$n1=range(50,80,1); $n2=range(80,100,1); $n3=range(70,90,1); $total=$n1+$n2+$n3; $ans1=decimal(0,$n1/$total*360); $ans2=decimal(0,$n2/$total*360); $ans3=decimal(0,$n3/$total*360);condition:eq($ans1+$ans2+$ans3,360);@ qu.3.2.weighting=1,1,1@ qu.3.2.numbering=alpha@ qu.3.2.part.1.name=$ans1@ qu.3.2.part.1.answer.units=@ qu.3.2.part.1.numStyle=thousands scientific arithmetic@ qu.3.2.part.1.editing=useHTML@ qu.3.2.part.1.showUnits=false@ qu.3.2.part.1.question=(Unset)@ qu.3.2.part.1.mode=Numeric@ qu.3.2.part.1.grading=exact_value@ qu.3.2.part.1.negStyle=minus@ qu.3.2.part.1.answer.num=$ans1@ qu.3.2.part.2.name=$ans2@ qu.3.2.part.2.answer.units=@ qu.3.2.part.2.numStyle=thousands scientific arithmetic@ qu.3.2.part.2.editing=useHTML@ qu.3.2.part.2.showUnits=false@ qu.3.2.part.2.question=(Unset)@ qu.3.2.part.2.mode=Numeric@ qu.3.2.part.2.grading=exact_value@ qu.3.2.part.2.negStyle=minus@ qu.3.2.part.2.answer.num=$ans2@ qu.3.2.part.3.name=$ans3@ qu.3.2.part.3.answer.units=@ qu.3.2.part.3.numStyle=thousands scientific arithmetic@ qu.3.2.part.3.editing=useHTML@ qu.3.2.part.3.showUnits=false@ qu.3.2.part.3.question=(Unset)@ qu.3.2.part.3.mode=Numeric@ qu.3.2.part.3.grading=exact_value@ qu.3.2.part.3.negStyle=minus@ qu.3.2.part.3.answer.num=$ans3@ qu.3.2.question=

Welkerville Middle School currently has $n1 6th grade students, $n2 7th grade students, and $n3 8th grade students. You have been asked to create a circle chart for this data. Find the angle (to the nearest degree) for each category.
Do not enter the degree symbol in the answer boxes.

6th Grade <1>

7th Grade <2>

8th Grade <3>

@ qu.4.topic=12_3_Interpret Line Graph Points@ qu.4.1.question=

A line graph of the enrollment at Welkerville Middle School for the years 2000-2005 is shown above. Use the graph to estimate the enrollment in the year ${numfmt("0000",$year)}.@ qu.4.1.answer.num=$ans@ qu.4.1.answer.units=@ qu.4.1.showUnits=false@ qu.4.1.grading=toler_abs@ qu.4.1.err=3@ qu.4.1.negStyle=minus@ qu.4.1.numStyle=thousands scientific dollars arithmetic@ qu.4.1.mode=Numeric@ qu.4.1.name=WMS@ qu.4.1.comment=

A line graph of the enrollment at Welkerville Middle School for the years 2000-2005 is shown above. Use the graph to estimate the enrollment in the year ${numfmt("0000",$year)}.

The enrollment is $ans. Acceptable answers would be between ${$ans-3} and ${$ans+3}.

@ qu.4.1.editing=useHTML@ qu.4.1.algorithm=$i=rint(6); $year=2000+$i; $ans=switch($i,95,80,105,85,72,90);@ qu.4.2.question=

A line graph of the average daily attendance at the Welkerville Cinema for the years 2000-2005 is shown above. Use the graph to estimate the enrollment in the year ${numfmt("0000",$year)}.@ qu.4.2.answer.num=$ans@ qu.4.2.answer.units=@ qu.4.2.showUnits=false@ qu.4.2.grading=toler_abs@ qu.4.2.err=3@ qu.4.2.negStyle=minus@ qu.4.2.numStyle=thousands scientific dollars arithmetic@ qu.4.2.mode=Numeric@ qu.4.2.name=cinema@ qu.4.2.comment=

A line graph of the average daily attendance at the Welkerville Cinema for the years 2000-2005 is shown above. Use the graph to estimate the enrollment in the year ${numfmt("0000",$year)}.

The attendance is $ans. Acceptable answers would be between ${$ans-3} and ${$ans+3}.

@ qu.4.2.editing=useHTML@ qu.4.2.algorithm=$i=rint(6); $year=2000+$i; $ans=switch($i,121,105,99,62,72,90);@ qu.5.topic=12_3 Line Graph Max/Min@ qu.5.1.question=

A line graph of the enrollment at Welkerville Middle School for the years 2000-2005 is shown above. Use the graph to estimate the $t enrollment over this time period.

@ qu.5.1.answer.num=$num@ qu.5.1.answer.units=@ qu.5.1.showUnits=false@ qu.5.1.grading=toler_abs@ qu.5.1.err=3@ qu.5.1.negStyle=minus@ qu.5.1.numStyle=thousands scientific dollars arithmetic@ qu.5.1.mode=Numeric@ qu.5.1.name=WMS max/min value@ qu.5.1.comment=

A line graph of the enrollment at Welkerville Middle School for the years 2000-2005 is shown above. Use the graph to estimate the $t enrollment over this time period.

The $t enrollment is $num. Acceptable answers would be between ${$num-3} and ${$num+3}.

@ qu.5.1.editing=useHTML@ qu.5.1.algorithm=$i=rint(2); $t=switch($i,"maximum","minimum"); $num=switch($i,105,72); $yr=switch($i,2002,2004);@ qu.5.2.question=

A line graph of the enrollment at Welkerville Middle School for the years 2000-2005 is shown above. Use the graph to find the year when the enrollment was a $t.

@ qu.5.2.answer.num=$yr@ qu.5.2.answer.units=@ qu.5.2.showUnits=false@ qu.5.2.grading=exact_value@ qu.5.2.negStyle=minus@ qu.5.2.numStyle=thousands scientific dollars arithmetic@ qu.5.2.mode=Numeric@ qu.5.2.name=WMS max/min year@ qu.5.2.comment=

A line graph of the enrollment at Welkerville Middle School for the years 2000-2005 is shown above. Use the graph to find the year which enrollment was at a $t.

The $t enrollment was in the year ${numfmt("0000",$yr)}.

@ qu.5.2.editing=useHTML@ qu.5.2.algorithm=$i=rint(2); $t=switch($i,"maximum","minimum"); $num=switch($i,105,72); $yr=switch($i,2002,2004);@ qu.5.3.question=

A line graph of the average daily attendance at the Welkerville Cinema for the years 2000-2005 is shown above. Use the graph to estimate the $t attendance over this time period.

@ qu.5.3.answer.num=$num@ qu.5.3.answer.units=@ qu.5.3.showUnits=false@ qu.5.3.grading=toler_abs@ qu.5.3.err=3@ qu.5.3.negStyle=minus@ qu.5.3.numStyle=thousands scientific dollars arithmetic@ qu.5.3.mode=Numeric@ qu.5.3.name=cinema max/min value@ qu.5.3.comment=

A line graph of the average daily attendance at the Welkerville Cinema for the years 2000-2005 is shown above. Use the graph to estimate the $t attendance over this time period.

The $t attendance is $num. Acceptable answers would be between ${$num-3} and ${$num+3}.

@ qu.5.3.editing=useHTML@ qu.5.3.algorithm=$i=rint(2); $t=switch($i,"maximum","minimum"); $num=switch($i,121,62); $yr=switch($i,2000,2003);@ qu.5.4.question=

A line graph of the average daily attendance at the Welkerville Cinema for the years 2000-2005 is shown above. Use the graph to find the year when the attendance was a $t.

@ qu.5.4.answer.num=$yr@ qu.5.4.answer.units=@ qu.5.4.showUnits=false@ qu.5.4.grading=exact_value@ qu.5.4.negStyle=minus@ qu.5.4.numStyle=thousands scientific dollars arithmetic@ qu.5.4.mode=Numeric@ qu.5.4.name=cinema max/min year@ qu.5.4.comment=

A line graph of the average daily attendance at the Welkerville Cinema for the years 2000-2005 is shown above. Use the graph to find the year when the attendance was a $t.

The $t attendance was in the year ${numfmt("0000",$yr)}.

@ qu.5.4.editing=useHTML@ qu.5.4.algorithm=$i=rint(2); $t=switch($i,"maximum","minimum"); $num=switch($i,105,72); $yr=switch($i,2000,2003);@ qu.6.topic=12_3 Line Graph Slope@ qu.6.1.mode=Non Permuting Multiple Selection@ qu.6.1.name=wms decrease@ qu.6.1.comment=

The enrollment increased from:
2001 to 2002 and 2004 to 2005
The enrollment decreased from:
2000 to 2001, 2002 to 2003, and 2003 to 2004

@ qu.6.1.editing=useHTML@ qu.6.1.question=

A line graph of the enrollment at Welkerville Middle School for the years 2000-2005 is shown above. Use the graph to determine when the enrollment decreased. Place a check in front of each interval over which the enrollment decreased. @ qu.6.1.answer=1, 3, 4@ qu.6.1.choice.1=2000-2001@ qu.6.1.choice.2=2001-2002@ qu.6.1.choice.3=2002-2003@ qu.6.1.choice.4=2003-2004@ qu.6.1.choice.5=2004-2005@ qu.6.2.mode=Non Permuting Multiple Selection@ qu.6.2.name=wms increase@ qu.6.2.comment=

The enrollment increased from:
2001 to 2002 and 2004 to 2005
The enrollment decreased from:
2000 to 2001, 2002 to 2003, and 2003 to 2004

@ qu.6.2.editing=useHTML@ qu.6.2.question=

A line graph of the enrollment at Welkerville Middle School for the years 2000-2005 is shown above. Use the graph to determine when the enrollment increased. Place a check in front of each interval over which the enrollment increased. @ qu.6.2.answer=2, 5@ qu.6.2.choice.1=2000-2001@ qu.6.2.choice.2=2001-2002@ qu.6.2.choice.3=2002-2003@ qu.6.2.choice.4=2003-2004@ qu.6.2.choice.5=2004-2005@ qu.6.3.mode=Non Permuting Multiple Selection@ qu.6.3.name=cinema decrease@ qu.6.3.comment=

A line graph of the average daily attendance at the Welkerville Cinema for the years 2000-2005 is shown above. Use the graph to determine when the enrollment decreased. Place a check in front of each interval over which the attendance decreased.

The attendance increased from:
2003 to 2004 and 2004 to 2005
The attendance decreased from:
2000 to 2001, 2001 to 2002, and 2002 to 2003

@ qu.6.3.editing=useHTML@ qu.6.3.question=

A line graph of the average daily attendance at the Welkerville Cinema for the years 2000-2005 is shown above. Use the graph to determine when the attendance decreased. Place a check in front of each interval over which the attendance decreased. @ qu.6.3.answer=1, 2, 3@ qu.6.3.choice.1=2000-2001@ qu.6.3.choice.2=2001-2002@ qu.6.3.choice.3=2002-2003@ qu.6.3.choice.4=2003-2004@ qu.6.3.choice.5=2004-2005@ qu.6.4.mode=Non Permuting Multiple Selection@ qu.6.4.name=cinema increase@ qu.6.4.comment=

A line graph of the average daily attendance at the Welkerville Cinema for the years 2000-2005 is shown above. Use the graph to determine when the enrollment increased. Place a check in front of each interval over which the attendance increased.

The attendance increased from:
2003 to 2004 and 2004 to 2005
The attendance increased from:
2000 to 2001, 2001 to 2002, and 2002 to 2003

@ qu.6.4.editing=useHTML@ qu.6.4.question=

A line graph of the average daily attendance at the Welkerville Cinema for the years 2000-2005 is shown above. Use the graph to determine when the attendance increased. Place a check in front of each interval over which the attendance increased. @ qu.6.4.answer=4, 5@ qu.6.4.choice.1=2000-2001@ qu.6.4.choice.2=2001-2002@ qu.6.4.choice.3=2002-2003@ qu.6.4.choice.4=2003-2004@ qu.6.4.choice.5=2004-2005@ qu.7.topic=12_4 Counting Principle A@ qu.7.1.question=How many different ways can a person have cherry, apple, or peach pie if the pie is ordered with or without ice cream?@ qu.7.1.answer.num=$ans@ qu.7.1.answer.units=@ qu.7.1.showUnits=false@ qu.7.1.grading=exact_value@ qu.7.1.negStyle=minus@ qu.7.1.numStyle=thousands scientific dollars arithmetic@ qu.7.1.mode=Numeric@ qu.7.1.name=Pie@ qu.7.1.comment=

How many different ways can a person have cherry, apple, or peach pie if the pie is ordered with or without ice cream?

There are $n1 pieces of pie and $n2 possible choices of ice cream or no ice cream.
$n1 � $n2 = $ans possible orders.

@ qu.7.1.editing=useHTML@ qu.7.1.algorithm=$n1=3; $n2=2; $ans=$n1*$n2;@ qu.7.2.question=T-shirts come in S, M, L, and XL. There are $n2 choices of color. How many different T-shirts are available?@ qu.7.2.answer.num=$ans@ qu.7.2.answer.units=@ qu.7.2.showUnits=false@ qu.7.2.grading=exact_value@ qu.7.2.negStyle=minus@ qu.7.2.numStyle=thousands scientific dollars arithmetic@ qu.7.2.mode=Numeric@ qu.7.2.name=T-Shirt@ qu.7.2.comment=

T-shirts come in S, M, L, and XL. Color choices are red, blue, and black. How many different T-shirts are available?

There are $n1 size and $n2 colors.
$n1 � $n2 = $ans possible shirts.

@ qu.7.2.editing=useHTML@ qu.7.2.algorithm=$n1=4; $n2=range(3,8,1); $ans=$n1*$n2;@ qu.7.3.question=A sport utility vehicle (SUV) comes in a choice of $n1 exterior colors and $n2 interior colors. How many possible color schemes are available for the SUV?@ qu.7.3.answer.num=$ans@ qu.7.3.answer.units=@ qu.7.3.showUnits=false@ qu.7.3.grading=exact_value@ qu.7.3.negStyle=minus@ qu.7.3.numStyle=thousands scientific dollars arithmetic@ qu.7.3.mode=Numeric@ qu.7.3.name=SUV@ qu.7.3.comment=

A sport utility vehicle (SUV) comes in a choice of $n1 exterior colors and $n2 interior colors. How many possible color schemes are available for the SUV?

$n1 � $n2 = $ans possible SUV's.

@ qu.7.3.editing=useHTML@ qu.7.3.algorithm=$n1=range(4,6,1); $n2=range(1,$n1-1,1); $ans=$n1*$n2;@ qu.7.4.question=A two-sided coin is tossed by $n1 people. How many different outcomes are possible?@ qu.7.4.answer.num=$ans@ qu.7.4.answer.units=@ qu.7.4.showUnits=false@ qu.7.4.grading=exact_value@ qu.7.4.negStyle=minus@ qu.7.4.numStyle=thousands scientific dollars arithmetic@ qu.7.4.mode=Numeric@ qu.7.4.name=coins@ qu.7.4.comment=

A two-sided coin is tossed by $n1 people. How many different outcomes are possible?

$n1 � $n2 = $ans possible outcomes.

@ qu.7.4.editing=useHTML@ qu.7.4.algorithm=$n1=range(4,12,1); $n2=2; $ans=$n1*$n2;@ qu.7.5.question=A bag contains $n1 numbered red balls. A second bag contains $n2 numbered white balls. How many different ways can a person draw one ball from each bag?@ qu.7.5.answer.num=$ans@ qu.7.5.answer.units=@ qu.7.5.showUnits=false@ qu.7.5.grading=exact_value@ qu.7.5.negStyle=minus@ qu.7.5.numStyle=thousands scientific dollars arithmetic@ qu.7.5.mode=Numeric@ qu.7.5.name=numbered balls@ qu.7.5.comment=

A bag contains $n1 numbered red balls. A second bag contains $n2 numbered white balls. How many different ways can a person draw one ball from each bag?

$n1 � $n2 = $ans possible outcomes.

@ qu.7.5.editing=useHTML@ qu.7.5.algorithm=$n1=range(8,15,1); $n2=range(4,12,1); $ans=$n1*$n2;@ qu.8.topic=12_4 Counting Principle B@ qu.8.1.question=A bag contains $n1 numbered red balls. A second bag contains $n2 numbered white balls. A third bag contains $n3 green balls. How many different ways can a person draw one ball from each bag?@ qu.8.1.answer.num=$ans@ qu.8.1.answer.units=@ qu.8.1.showUnits=false@ qu.8.1.grading=exact_value@ qu.8.1.negStyle=minus@ qu.8.1.numStyle=thousands scientific dollars arithmetic@ qu.8.1.mode=Numeric@ qu.8.1.name=Numbered Balls@ qu.8.1.comment=

A bag contains $n1 numbered red balls. A second bag contains $n2 numbered white balls. A third bag contains $n3 green balls. How many different ways can a person draw one ball from each bag?

$n1 � $n2 � $n3 = $ans possible outcomes.

@ qu.8.1.editing=useHTML@ qu.8.1.algorithm=$n1=range(8,15,1); $n2=range(4,12,1); $n3=range(5,8,1); $ans=$n1*$n2*$n3;@ qu.8.2.question=A password must contain two letters A-Z which may followed by two numbers 0-9. The letters and numbers may repeat. How many different passwords are possible?@ qu.8.2.answer.num=$ans@ qu.8.2.answer.units=@ qu.8.2.showUnits=false@ qu.8.2.grading=exact_value@ qu.8.2.negStyle=minus@ qu.8.2.numStyle=thousands scientific dollars arithmetic@ qu.8.2.mode=Numeric@ qu.8.2.name=Password@ qu.8.2.comment=

A password must contain two letters A-Z which may followed by two numbers 0-9. The letters and numbers may repeat. How many different passwords are possible?

There are 26 letters and 10 numbers.

There are 26 • 26 • 10 • 10 = $ans

@ qu.8.2.editing=useHTML@ qu.8.2.algorithm=$ans=26*26*10*10@ qu.8.3.question=In a closet are $n1 shirts, $n2 pants and $n3 pairs of shoes. How many different ways can a person put together an outfit?@ qu.8.3.answer.num=$ans@ qu.8.3.answer.units=@ qu.8.3.showUnits=false@ qu.8.3.grading=exact_value@ qu.8.3.negStyle=minus@ qu.8.3.numStyle=thousands scientific dollars arithmetic@ qu.8.3.mode=Numeric@ qu.8.3.name=Outfits@ qu.8.3.comment=

In a closet are $n1 shirts, $n2 pants and $n3 pairs of shoes. How many different ways can a person put together an outfit?

There are $n1 • $n2 • $n3 = $ans outfits.

@ qu.8.3.editing=useHTML@ qu.8.3.algorithm=$n1=range(8,12,1);$n2=range(4,7,1);$n3=range(2,3,1);$ans=$n1*$n2*$n3;@ qu.8.4.question=Welkerville has $n1 different movie theaters. Each theatre has $n2 screens showing movies $n3 times per day. How many different choices are available to go to a movie?@ qu.8.4.answer.num=$ans@ qu.8.4.answer.units=@ qu.8.4.showUnits=false@ qu.8.4.grading=exact_value@ qu.8.4.negStyle=minus@ qu.8.4.numStyle=thousands scientific dollars arithmetic@ qu.8.4.mode=Numeric@ qu.8.4.name=Movie@ qu.8.4.comment=

Welkerville has $n1 different movie theaters. Each theatre has $n2 screens showing movies $n3 times per day. How many different choices are available to go to a movie?

There are $n1 • $n2 • $n3 = $ans movie times.

@ qu.8.4.editing=useHTML@ qu.8.4.algorithm=$n1=range(4,7,1);$n2=range(3,4);$n3=range(3,5,1);$ans=$n1*$n2*$n3;@ qu.9.topic=12_4 Probability A@ qu.9.1.mode=Inline@ qu.9.1.name=coins@ qu.9.1.comment=The number of possible outcomes is two for each of the $n1 persons.
Outcomes = 2 times itself $n1 times = $an = 2^$n1 = ${2^$n1}.
The number of favorable outcomes where each person tosses a head is 1.
The probability is ${$n}/${$d}.@ qu.9.1.editing=useHTML@ qu.9.1.algorithm=$n1=range(3,6,1); $d=2^$n1; $n=1; $an=switch($n1-3,"2 • 2 • 2","2 • 2 • 2 • 2","2 • 2 • 2 • 2 • 2","2 • 2 • 2 • 2 • 2 • 2");@ qu.9.1.weighting=1,1@ qu.9.1.numbering=alpha@ qu.9.1.part.1.name=$n@ qu.9.1.part.1.answer.units=@ qu.9.1.part.1.numStyle=thousands scientific arithmetic@ qu.9.1.part.1.editing=useHTML@ qu.9.1.part.1.showUnits=false@ qu.9.1.part.1.question=(Unset)@ qu.9.1.part.1.mode=Numeric@ qu.9.1.part.1.grading=exact_value@ qu.9.1.part.1.negStyle=minus@ qu.9.1.part.1.answer.num=$n@ qu.9.1.part.2.name=$d@ qu.9.1.part.2.answer.units=@ qu.9.1.part.2.numStyle=thousands scientific arithmetic@ qu.9.1.part.2.editing=useHTML@ qu.9.1.part.2.showUnits=false@ qu.9.1.part.2.question=(Unset)@ qu.9.1.part.2.mode=Numeric@ qu.9.1.part.2.grading=exact_value@ qu.9.1.part.2.negStyle=minus@ qu.9.1.part.2.answer.num=$d@ qu.9.1.question=

A coin is flipped by $n1 persons. What is the probability of all individuals tossing a head?

Write your answer as a fraction in reduced form.

<1>

<2>

@ qu.9.2.mode=Inline@ qu.9.2.name=number cubes@ qu.9.2.comment=The number of possible outcomes is $a for each of the $n1 number cubes.
Outcomes = $a times itself $n1 times = $an = $a^$n1 = ${$a^$n1}.
The number of favorable outcomes where each person tosses a $n2 is 1.
The probability is ${$n}/${$d}.@ qu.9.2.editing=useHTML@ qu.9.2.algorithm=$n1=range(3,6,1); $d=6^$n1; $n=1; $a=6; $n2=range(1,6,1); $an=switch($n1-3,"$a • $a • $a","$a • $a • $a • $a","$a • $a • $a • $a • $a","$a • $a • $a • $a • $a • $a");@ qu.9.2.weighting=1,1@ qu.9.2.numbering=alpha@ qu.9.2.part.1.name=$n@ qu.9.2.part.1.answer.units=@ qu.9.2.part.1.numStyle=thousands scientific arithmetic@ qu.9.2.part.1.editing=useHTML@ qu.9.2.part.1.showUnits=false@ qu.9.2.part.1.question=(Unset)@ qu.9.2.part.1.mode=Numeric@ qu.9.2.part.1.grading=exact_value@ qu.9.2.part.1.negStyle=minus@ qu.9.2.part.1.answer.num=$n@ qu.9.2.part.2.name=$d@ qu.9.2.part.2.answer.units=@ qu.9.2.part.2.numStyle=thousands scientific arithmetic@ qu.9.2.part.2.editing=useHTML@ qu.9.2.part.2.showUnits=false@ qu.9.2.part.2.question=(Unset)@ qu.9.2.part.2.mode=Numeric@ qu.9.2.part.2.grading=exact_value@ qu.9.2.part.2.negStyle=minus@ qu.9.2.part.2.answer.num=$d@ qu.9.2.question=

A person rolls $n1 number cubes. What is the probability of all number cubes landing on a $n2?

Write your answer as a fraction in reduced form.

<1>

<2>

@ qu.10.topic=12_4 Probability B@ qu.10.1.mode=Inline@ qu.10.1.name=coins@ qu.10.1.comment=The number of possible outcomes is two for each of the $n1 persons.
Outcomes = 2 times itself $n1 times = $an = 2^$n1 = ${2^$n1}.
The number of favorable outcomes where each person tosses a head is 2. They can all land heads or all land tails.
The probability is ${$num}/${$den}. The greatest common factor is $g. The reduced fraction is ${$n}/${$d}.@ qu.10.1.editing=useHTML@ qu.10.1.algorithm=$n1=range(3,6,1); $den=2^$n1; $num=2;$g=gcd($den,$num);$n=$num/$g;$d=$den/$g; $an=switch($n1-3,"2 • 2 • 2","2 • 2 • 2 • 2","2 • 2 • 2 • 2 • 2","2 • 2 • 2 • 2 • 2 • 2");@ qu.10.1.weighting=1,1@ qu.10.1.numbering=alpha@ qu.10.1.part.1.name=$n@ qu.10.1.part.1.answer.units=@ qu.10.1.part.1.numStyle=thousands scientific arithmetic@ qu.10.1.part.1.editing=useHTML@ qu.10.1.part.1.showUnits=false@ qu.10.1.part.1.question=(Unset)@ qu.10.1.part.1.mode=Numeric@ qu.10.1.part.1.grading=exact_value@ qu.10.1.part.1.negStyle=minus@ qu.10.1.part.1.answer.num=$n@ qu.10.1.part.2.name=$d@ qu.10.1.part.2.answer.units=@ qu.10.1.part.2.numStyle=thousands scientific arithmetic@ qu.10.1.part.2.editing=useHTML@ qu.10.1.part.2.showUnits=false@ qu.10.1.part.2.question=(Unset)@ qu.10.1.part.2.mode=Numeric@ qu.10.1.part.2.grading=exact_value@ qu.10.1.part.2.negStyle=minus@ qu.10.1.part.2.answer.num=$d@ qu.10.1.question=

A coin is flipped by $n1 persons. What is the probability of all coins landing with the same side facing up?

Write your answer as a fraction in reduced form.

<1>

<2>

@ qu.10.2.mode=Inline@ qu.10.2.name=number cubes@ qu.10.2.comment=The number of possible outcomes is $a for each of the $n1 number cubes.
Outcomes = $a times itself $n1 times = $an = $a^$n1 = ${$a^$n1}.
The number of favorable outcomes where each cube lands on the same value. They can all be 1, 2 , 3, 4, 5, or 6. There are 6 possible favorable outcomes.
The probability is ${$num}/${$den}. The greatest common factor is $g. The reduced fraction is ${$n}/${$d}.@ qu.10.2.editing=useHTML@ qu.10.2.algorithm=$n1=range(3,6,1);$a=6;$den=$a^$n1; $num=$a;$g=gcd($den,$num);$n=$num/$g;$d=$den/$g; $n2=range(1,6,1); $an=switch($n1-3,"$a • $a • $a","$a • $a • $a • $a","$a • $a • $a • $a • $a","$a • $a • $a • $a • $a • $a");@ qu.10.2.weighting=1,1@ qu.10.2.numbering=alpha@ qu.10.2.part.1.name=$n@ qu.10.2.part.1.answer.units=@ qu.10.2.part.1.numStyle=thousands scientific arithmetic@ qu.10.2.part.1.editing=useHTML@ qu.10.2.part.1.showUnits=false@ qu.10.2.part.1.question=(Unset)@ qu.10.2.part.1.mode=Numeric@ qu.10.2.part.1.grading=exact_value@ qu.10.2.part.1.negStyle=minus@ qu.10.2.part.1.answer.num=$n@ qu.10.2.part.2.name=$d@ qu.10.2.part.2.answer.units=@ qu.10.2.part.2.numStyle=thousands scientific arithmetic@ qu.10.2.part.2.editing=useHTML@ qu.10.2.part.2.showUnits=false@ qu.10.2.part.2.question=(Unset)@ qu.10.2.part.2.mode=Numeric@ qu.10.2.part.2.grading=exact_value@ qu.10.2.part.2.negStyle=minus@ qu.10.2.part.2.answer.num=$d@ qu.10.2.question=

A person rolls $n1 number cubes. What is the probability of all number cubes landing on the same value?

Write your answer as a fraction in reduced form.

<1>

<2>

@ qu.11.topic=12_8 Independent Probability@ qu.11.1.mode=Inline@ qu.11.1.name=Red Green@ qu.11.1.comment=

A bag contains $n1 red marbles and $n2 green marbles. What is the probability of drawing a red marble, replacing the marble and drawing a green marble?
Write your answer as a reduced fraction in the answer boxes.

There are $total marbles with $n1 red marbles.

The probability of drawing a red marble is

$n1

$total

The marble is replaced so there are still $total marbles in the bag. There are $n2 green marbles.

The probability of drawing a red marble is

$n2

$total

The probability of drawing a red followed by a green with replacement is

$n1

$total

•

$n2

$total

${$n1*$n2}

${$total^2}

The greatest common factor is $g. Reduced the fraction is

@ qu.11.1.editing=useHTML@ qu.11.1.algorithm=$n1=range(8,12,1); $n2=range(-1,1,2)*range(2,5,1)+$n1; $total=$n1+$n2; $g=gcd($n1*$n2,$total^2); $n=($n1*$n2)/$g; $d=($total^2)/$g;@ qu.11.1.weighting=1,1@ qu.11.1.numbering=alpha@ qu.11.1.part.1.name=$n@ qu.11.1.part.1.answer.units=@ qu.11.1.part.1.numStyle=thousands scientific arithmetic@ qu.11.1.part.1.editing=useHTML@ qu.11.1.part.1.showUnits=false@ qu.11.1.part.1.question=(Unset)@ qu.11.1.part.1.mode=Numeric@ qu.11.1.part.1.grading=exact_value@ qu.11.1.part.1.negStyle=minus@ qu.11.1.part.1.answer.num=$n@ qu.11.1.part.2.name=$d@ qu.11.1.part.2.answer.units=@ qu.11.1.part.2.numStyle=thousands scientific arithmetic@ qu.11.1.part.2.editing=useHTML@ qu.11.1.part.2.showUnits=false@ qu.11.1.part.2.question=(Unset)@ qu.11.1.part.2.mode=Numeric@ qu.11.1.part.2.grading=exact_value@ qu.11.1.part.2.negStyle=minus@ qu.11.1.part.2.answer.num=$d@ qu.11.1.question=

<1>

<2>

@ qu.11.2.mode=Inline@ qu.11.2.name=Green Green@ qu.11.2.comment=

A bag contains $n1 red marbles and $n2 green marbles. What is the probability of drawing a green marble, replacing the marble and drawing a green marble?
Write your answer as a reduced fraction in the answer boxes.

There are $total marbles.

The marble is replaced so there are always $total marbles in the bag. There are $n2 green marbles.

The probability of drawing a green marble is

$n2

$total

The probability of drawing a green followed by a green with replacement is

$n2

$total

•

$n2

$total

${$n2*$n2}

${$total^2}

The greatest common factor is $g. Reduced the fraction is

@ qu.11.2.editing=useHTML@ qu.11.2.algorithm=$n1=range(4,8,1); $n2=range(-1,1,2)*range(1,3,1)+$n1; $total=$n1+$n2; $g=gcd($n2*$n2,$total^2); $n=($n2*$n2)/$g; $d=($total^2)/$g;@ qu.11.2.weighting=1,1@ qu.11.2.numbering=alpha@ qu.11.2.part.1.name=$n@ qu.11.2.part.1.answer.units=@ qu.11.2.part.1.numStyle=thousands scientific arithmetic@ qu.11.2.part.1.editing=useHTML@ qu.11.2.part.1.showUnits=false@ qu.11.2.part.1.question=(Unset)@ qu.11.2.part.1.mode=Numeric@ qu.11.2.part.1.grading=exact_value@ qu.11.2.part.1.negStyle=minus@ qu.11.2.part.1.answer.num=$n@ qu.11.2.part.2.name=$d@ qu.11.2.part.2.answer.units=@ qu.11.2.part.2.numStyle=thousands scientific arithmetic@ qu.11.2.part.2.editing=useHTML@ qu.11.2.part.2.showUnits=false@ qu.11.2.part.2.question=(Unset)@ qu.11.2.part.2.mode=Numeric@ qu.11.2.part.2.grading=exact_value@ qu.11.2.part.2.negStyle=minus@ qu.11.2.part.2.answer.num=$d@ qu.11.2.question=

A bag contains $n1 red marbles and $n2 green marbles. What is the probability of drawing a green marble, replacing the marble and drawing another green marble?
Write your answer as a reduced fraction in the answer boxes.

<1>

<2>

@ qu.11.3.mode=Inline@ qu.11.3.name=Ring Toss@ qu.11.3.comment=

In a ring toss game using red rings, the chances of winning is $n1 in $d1 tosses. Using green rings, the changes of winning is $n2 in $d2 tosses. What is the probability of winning with a red ring followed by a green ring?
Write your answer as a reduced fraction in the answer boxes.

The probability of a winning red ring is

$n1

$d1

The probability of tossing a green ring is

$n2

$d2

The probability of tossing a winning red ring followed by a winning green ring is

$n1

$d1

•

$n2

$d2

${$n1*$n2}

${$total}

The greatest common factor is $g. Reduced the fraction is

@ qu.11.3.editing=useHTML@ qu.11.3.algorithm=$n1=range(1,3,2);$d1=range(5,7,2); $n2=range(3,5,2);$d2=range(11,13,1); $total=$d2*$d1; $g=gcd($n1*$n2,$total^2); $n=($n1*$n2)/$g; $d=($total)/$g;@ qu.11.3.weighting=1,1@ qu.11.3.numbering=alpha@ qu.11.3.part.1.name=$n@ qu.11.3.part.1.answer.units=@ qu.11.3.part.1.numStyle=thousands scientific arithmetic@ qu.11.3.part.1.editing=useHTML@ qu.11.3.part.1.showUnits=false@ qu.11.3.part.1.question=(Unset)@ qu.11.3.part.1.mode=Numeric@ qu.11.3.part.1.grading=exact_value@ qu.11.3.part.1.negStyle=minus@ qu.11.3.part.1.answer.num=$n@ qu.11.3.part.2.name=$d@ qu.11.3.part.2.answer.units=@ qu.11.3.part.2.numStyle=thousands scientific arithmetic@ qu.11.3.part.2.editing=useHTML@ qu.11.3.part.2.showUnits=false@ qu.11.3.part.2.question=(Unset)@ qu.11.3.part.2.mode=Numeric@ qu.11.3.part.2.grading=exact_value@ qu.11.3.part.2.negStyle=minus@ qu.11.3.part.2.answer.num=$d@ qu.11.3.question=

<1>

<2>

@ qu.12.topic=12_8 Dependent Probability@ qu.12.1.mode=Inline@ qu.12.1.name=Red Green@ qu.12.1.comment=

A bag contains $n1 red marbles and $n2 green marbles. What is the probability of drawing a red marble, placing the marble in your pocket and drawing a green marble?
Write your answer as a reduced fraction in the answer boxes.

The total number of marbles is $d1.

The probability of a red marble is

$n1

$d1

The marble is not replaced so there are $d2 marbles in the bag. There are $n2 green marbles.

The probability of drawing a green marble is

$n2

$d2

The probability of drawing a red followed by a green without replacement is

$n1

$d1

•

$n2

$d2

${$n1*$n2}

${$total}

The greatest common factor is $g. Reduced the fraction is

@ qu.12.1.editing=useHTML@ qu.12.1.algorithm=$n1=range(8,12,1); $n2=range(6,10,1); $d1=$n1+$n2;$d2=$d1-1;$total=$d1*$d2; $g=gcd($n1*$n2,$total); $n=($n1*$n2)/$g; $d=($total)/$g;@ qu.12.1.weighting=1,1@ qu.12.1.numbering=alpha@ qu.12.1.part.1.name=$n@ qu.12.1.part.1.answer.units=@ qu.12.1.part.1.numStyle=thousands scientific arithmetic@ qu.12.1.part.1.editing=useHTML@ qu.12.1.part.1.showUnits=false@ qu.12.1.part.1.question=(Unset)@ qu.12.1.part.1.mode=Numeric@ qu.12.1.part.1.grading=exact_value@ qu.12.1.part.1.negStyle=minus@ qu.12.1.part.1.answer.num=$n@ qu.12.1.part.2.name=$d@ qu.12.1.part.2.answer.units=@ qu.12.1.part.2.numStyle=thousands scientific arithmetic@ qu.12.1.part.2.editing=useHTML@ qu.12.1.part.2.showUnits=false@ qu.12.1.part.2.question=(Unset)@ qu.12.1.part.2.mode=Numeric@ qu.12.1.part.2.grading=exact_value@ qu.12.1.part.2.negStyle=minus@ qu.12.1.part.2.answer.num=$d@ qu.12.1.question=

<1>

<2>

@ qu.12.2.mode=Inline@ qu.12.2.name=Green Green@ qu.12.2.comment=

A bag contains $n1 red marbles and $n2 green marbles. What is the probability of drawing a green marble, placing the marble in your pocket and drawing a green marble?
Write your answer as a reduced fraction in the answer boxes.

The total number of marbles is $d1.

The probability of a green marble is

$n2

$d1

The marble is not replaced so there are $d2 marbles in the bag. There are ${$n2-1} green marbles.

The probability of drawing a green marble is

${$n2-1}

$d2

The probability of drawing a green followed by a green without replacement is

$n2

$d1

•

${$n2-1}

$d2

${$n1*($n2-1)}

${$total}

The greatest common factor is $g. Reduced the fraction is

@ qu.12.2.editing=useHTML@ qu.12.2.algorithm=$n1=range(8,12,1); $n2=range(6,10,1); $d1=$n1+$n2;$d2=$d1-1;$total=$d1*$d2; $g=gcd($n2*($n2-1),$total); $n=($n2*($n2-1))/$g; $d=($total)/$g;@ qu.12.2.weighting=1,1@ qu.12.2.numbering=alpha@ qu.12.2.part.1.name=$n@ qu.12.2.part.1.answer.units=@ qu.12.2.part.1.numStyle=thousands scientific arithmetic@ qu.12.2.part.1.editing=useHTML@ qu.12.2.part.1.showUnits=false@ qu.12.2.part.1.question=(Unset)@ qu.12.2.part.1.mode=Numeric@ qu.12.2.part.1.grading=exact_value@ qu.12.2.part.1.negStyle=minus@ qu.12.2.part.1.answer.num=$n@ qu.12.2.part.2.name=$d@ qu.12.2.part.2.answer.units=@ qu.12.2.part.2.numStyle=thousands scientific arithmetic@ qu.12.2.part.2.editing=useHTML@ qu.12.2.part.2.showUnits=false@ qu.12.2.part.2.question=(Unset)@ qu.12.2.part.2.mode=Numeric@ qu.12.2.part.2.grading=exact_value@ qu.12.2.part.2.negStyle=minus@ qu.12.2.part.2.answer.num=$d@ qu.12.2.question=

<1>

<2>

@ qu.13.topic=12_8 Probability@ qu.13.1.mode=Inline@ qu.13.1.name=book report@ qu.13.1.comment=

You are a member of a class of $n1 students. $n2 have already given their book report. What is the probability of you will be called upon next to provide your book report?
Write your answer as a reduced fraction in the answer boxes.

The total number of students who have not given a book report is ${$n1-$n2}.

The probability of a being called next is

${$n1-$n2}

@ qu.13.1.editing=useHTML@ qu.13.1.algorithm=$n1=range(16,30,1); $n2=range(2,$n1/2-1,1); $n=1;$d=$n1-$n2;@ qu.13.1.weighting=1,1@ qu.13.1.numbering=alpha@ qu.13.1.part.1.name=$n@ qu.13.1.part.1.answer.units=@ qu.13.1.part.1.numStyle=thousands scientific arithmetic@ qu.13.1.part.1.editing=useHTML@ qu.13.1.part.1.showUnits=false@ qu.13.1.part.1.question=(Unset)@ qu.13.1.part.1.mode=Numeric@ qu.13.1.part.1.grading=exact_value@ qu.13.1.part.1.negStyle=minus@ qu.13.1.part.1.answer.num=$n@ qu.13.1.part.2.name=$d@ qu.13.1.part.2.answer.units=@ qu.13.1.part.2.numStyle=thousands scientific arithmetic@ qu.13.1.part.2.editing=useHTML@ qu.13.1.part.2.showUnits=false@ qu.13.1.part.2.question=(Unset)@ qu.13.1.part.2.mode=Numeric@ qu.13.1.part.2.grading=exact_value@ qu.13.1.part.2.negStyle=minus@ qu.13.1.part.2.answer.num=$d@ qu.13.1.question=

<1>

<2>

@ qu.13.2.mode=Inline@ qu.13.2.name=number cube@ qu.13.2.comment=

What is the probability of rolling a number cube 3 times and having the rolls be $n1, $n2, and $n3 in order?
Write your answer as a reduced fraction in the answer boxes.

Each number cube has 6 numbers..

The probability of rolling any particular number is

The probability of rolling any combination of 3 numbers is

•

216

@ qu.13.2.editing=useHTML@ qu.13.2.algorithm=$n1=range(1,6,1); $n2=range(1,6,1); $n3=range(1,6,1);$n=1;$d=216;@ qu.13.2.weighting=1,1@ qu.13.2.numbering=alpha@ qu.13.2.part.1.name=$n@ qu.13.2.part.1.answer.units=@ qu.13.2.part.1.numStyle=thousands scientific arithmetic@ qu.13.2.part.1.editing=useHTML@ qu.13.2.part.1.showUnits=false@ qu.13.2.part.1.question=(Unset)@ qu.13.2.part.1.mode=Numeric@ qu.13.2.part.1.grading=exact_value@ qu.13.2.part.1.negStyle=minus@ qu.13.2.part.1.answer.num=$n@ qu.13.2.part.2.name=$d@ qu.13.2.part.2.answer.units=@ qu.13.2.part.2.numStyle=thousands scientific arithmetic@ qu.13.2.part.2.editing=useHTML@ qu.13.2.part.2.showUnits=false@ qu.13.2.part.2.question=(Unset)@ qu.13.2.part.2.mode=Numeric@ qu.13.2.part.2.grading=exact_value@ qu.13.2.part.2.negStyle=minus@ qu.13.2.part.2.answer.num=$d@ qu.13.2.question= What is the probability of rolling a number cube 3 times and having the rolls be $n1, $n2, and $n3 in order?
Write your answer as a reduced fraction in the answer boxes.

<1>

<2>

@ qu.13.3.mode=Inline@ qu.13.3.name=cookies@ qu.13.3.comment=

There are $n1 sugar cookies, $n2 chocolate chip cookies, and $n3 frosted cookies in a cookie jar. What is the probability of drawing a sugar cookie, eating it and choosing a frosted cookie?
Write your answer as a reduced fraction in the answer boxes.

There are ${$n1+$n2+$n3} cookies in the jar.

The probability of choosing a sugar cookie is

$n1

${$n1+$n2+$n3}

There are now ${$n1+$n2+$n3-1} cookies in the jar.

The probability of choosing a frosted cookie is

$n3

${$n1+$n2+$n3-1}

The probability of choosing a sugar cookie followed by a frosted cookie is

$n1

${$n1+$n2+$n3}

•

$n3

${$n1+$n2+$n3-1}

${$n1*$n3}

${($n1+$n2+$n3)*($n1+$n2+$n3-1)}

The greatest common factor is $g. The probability in reduced form is

@ qu.13.3.editing=useHTML@ qu.13.3.algorithm=$n1=range(2,6,1); $n2=range(2,6,1); $n3=range(2,6,1);$g=gcd(($n1*$n3),($n1+$n2+$n3)*($n1+$n2+$n3-1));$n=($n1*$n3)/$g;$d=($n1+$n2+$n3)*($n1+$n2+$n3-1)/$g;@ qu.13.3.weighting=1,1@ qu.13.3.numbering=alpha@ qu.13.3.part.1.name=$n@ qu.13.3.part.1.answer.units=@ qu.13.3.part.1.numStyle=thousands scientific arithmetic@ qu.13.3.part.1.editing=useHTML@ qu.13.3.part.1.showUnits=false@ qu.13.3.part.1.question=(Unset)@ qu.13.3.part.1.mode=Numeric@ qu.13.3.part.1.grading=exact_value@ qu.13.3.part.1.negStyle=minus@ qu.13.3.part.1.answer.num=$n@ qu.13.3.part.2.name=$d@ qu.13.3.part.2.answer.units=@ qu.13.3.part.2.numStyle=thousands scientific arithmetic@ qu.13.3.part.2.editing=useHTML@ qu.13.3.part.2.showUnits=false@ qu.13.3.part.2.question=(Unset)@ qu.13.3.part.2.mode=Numeric@ qu.13.3.part.2.grading=exact_value@ qu.13.3.part.2.negStyle=minus@ qu.13.3.part.2.answer.num=$d@ qu.13.3.question= There are $n1 sugar cookies, $n2 chocolate chip cookies, and $n3 frosted cookies in a cookie jar. What is the probability of drawing a sugar cookie, eating it and choosing a frosted cookie?
Write your answer as a reduced fraction in the answer boxes.

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@ qu.13.4.mode=Inline@ qu.13.4.name=cookies - 2 of same kind@ qu.13.4.comment=

There are $n1 sugar cookies, $n2 chocolate chip cookies, and $n3 frosted cookies in a cookie jar. What is the probability of drawing a chocolate chip cookie, eating it and choosing another chocolate chip cookie?
Write your answer as a reduced fraction in the answer boxes.

There are ${$n1+$n2+$n3} cookies in the jar.

The probability of choosing a chocolate chip cookie is

$n2

${$n1+$n2+$n3}

There are now ${$n1+$n2+$n3-1} cookies in the jar with ${$n2-1} chocolate chip cookies.

The probability of choosing a second chocolate chip cookie is

${$n2-1}

${$n1+$n2+$n3-1}

The probability of choosing two chocolate chip cookies is

$n2

${$n1+$n2+$n3}

•

${$n2-1}

${$n1+$n2+$n3-1}

${$n2*($n2-1)}

${($n1+$n2+$n3)*($n1+$n2+$n3-1)}

The greatest common factor is $g. The probability in reduced form is

@ qu.13.4.editing=useHTML@ qu.13.4.algorithm=$n1=range(2,6,1); $n2=range(2,6,1); $n3=range(2,6,1);$g=gcd(($n2*($n2-1)),($n1+$n2+$n3)*($n1+$n2+$n3-1));$n=($n2*($n2-1))/$g;$d=($n1+$n2+$n3)*($n1+$n2+$n3-1)/$g;@ qu.13.4.weighting=1,1@ qu.13.4.numbering=alpha@ qu.13.4.part.1.name=$n@ qu.13.4.part.1.answer.units=@ qu.13.4.part.1.numStyle=thousands scientific arithmetic@ qu.13.4.part.1.editing=useHTML@ qu.13.4.part.1.showUnits=false@ qu.13.4.part.1.question=(Unset)@ qu.13.4.part.1.mode=Numeric@ qu.13.4.part.1.grading=exact_value@ qu.13.4.part.1.negStyle=minus@ qu.13.4.part.1.answer.num=$n@ qu.13.4.part.2.name=$d@ qu.13.4.part.2.answer.units=@ qu.13.4.part.2.numStyle=thousands scientific arithmetic@ qu.13.4.part.2.editing=useHTML@ qu.13.4.part.2.showUnits=false@ qu.13.4.part.2.question=(Unset)@ qu.13.4.part.2.mode=Numeric@ qu.13.4.part.2.grading=exact_value@ qu.13.4.part.2.negStyle=minus@ qu.13.4.part.2.answer.num=$d@ qu.13.4.question= There are $n1 sugar cookies, $n2 chocolate chip cookies, and $n3 frosted cookies in a cookie jar. What is the probability of drawing a chocolate chip cookie, eating it and choosing another chocolate chip cookie?
Write your answer as a reduced fraction in the answer boxes.

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