Unit 8 Day 8 & 9 Sample Space & Probability Practice

Last updated over 4 years ago

30 questions

A local restaurant offers a Prix Fixe menu, with a choice of an appertizer, an entree and a desert for one price.
If there are 3 choices for the appetizer, 5 choices for the entree and 4 choices for dessert, how many different meals can be ordered?

Categorize the situations as involving a permutation or a combination:

100 runners finish a race in 1st - 10th place.
The top 10 finished in a preliminary auto race will qualify for the final race.
13 books arranged on a shelf at the library
Two students, from the class of 385 Seniors, are the Valedictorian(#1 class rankk), and Salutatorian (#2 class rank), they give speeches at graduation.
At football practice, 1/2 the team is chosen to work out in the weight room, the other half are sent out to the field to run drills.
An animal shelter chooses 3 kittens to put in the adopt-a-pet segment on the local news.
A teacher assigns 3 students out of a class of 20 to work on a class data project.

Permutation
Combination

A casino claims that its Roulette Wheel is truly random.
What should that claim mean about the roulette wheel and its sections & colors?

Explain below:

A doctor tells a patient just diagnosed with a serious disease that there's a 60% chance she'll live at least 5 years.
Where do you think that probability comes from?
(interpret this probability, remember our answers to the class kick from last week Thurs/Fri)

After an unusually dry autumn, a rado announcer is hear to say:
'Watch out! We'll pay for these sunny days later on this winter.'

Explain what he's trying to say and comment on the validity of his reasoning.
Ex. what law is he using? Is his thinking flawed? Why?

Commercial airplanes have excellent safety records, nevertheless there are crashes occasionally, with the loss of many lives. In the weeks following a crash, airlines often report a drop in the number of passengers, probabily becausepeople are afraid to risk flying.
A travel agent suggests that since the law of averages makes it highly unlikely to have two crashes within a few weeks of each other, flying soon after a crash is the safest time to fly.

Do you agree? Why or why not?
Think about the laws we have discussed in class.

You randomly choose 2 spices off a spice rack to complete your chili recipe.
There are 20 spices on the rack. How many recipes are possible?
First:
Is this a permutation or combination?
Why?

You randomly choose 2 spices off a spice rack to complete your chili recipe.
There are 20 spices on the rack. How many recipes are possible?

Second:
What formula would you use in the calculator?
Math, Prob, .... what do you choose?

Use the 'math keyboard' to enter the set up for either the permutation or combination,
use the box with a subscript on the far right, 2nd row down, to enter the numbers,
use the arrow key to get out of the subscript level.

You randomly choose 2 spices off a spice rack to complete your chili recipe.
There are 20 spices on the rack. How many recipes are possible?

Use your TI-84 calculator to find the answer.

How many different chili recipes are possible? (this is a sample space)

How many different ways can you choose two spices from the following list:
cumin, red pepper, cinnamon, celery seed or thyme?

First:
What function will you use in the calculator? Enter it below with the math keyboard.

How many different ways can you choose two spices from the following list of 5 spices:
cumin, red pepper, cinnamon, celery seed or thyme?

Use your TI-84 to calculate the number of ways you can randomly choose the two spices from the group of 5.

Use your answers to #3 (the total number of possible ways to choose 5 spices) and #5 (the total number of ways to choose 2 from the 5), what is the probability that the spices you choose for your chili are two from this list: cumin, red pepper, cinnamon, celery seed or thyme.

Hint:

Round your answer to three places past the decimal, write as a percent.

The 5 Smith children run to the ice cream truck. In how many orders can they be served one at a time (they stand in line)
First:
Is this a permutation or combination?
Why?

The 5 Smith children run to the ice cream truck. In how many orders can they be served one at a time (they stand in line)
Second:
What formula would you use in the calculator?
Math, Prob, .... what do you choose?
Use the 'math keyboard' to enter the set up for either the permutation or combination,
use the box with a subscript on the far right to enter the numbers,
use the arrow key to get out of the subscript level.

The 5 Smith children run to the ice cream truck. In how many orders can they be served one at a time (they stand in line)

Use your TI-84 calculator to find the answer.
How many different ways can the Smith children stand in line for ice cream? (this is a sample space)

The 5 Smith children run to the ice cream truck. If the two oldest children are served first, how many different ways can they line up?

Hint: you can use the Fundamental Counting Principle in this situation.

How many different ways can the Smith children stand in line for ice cream with the oldest two children first and the three youngest children next?

Think: how many combinations with the oldest 2 children and # combinations with the youngest 3 children

What is the probability that the Smith children will line up with the two oldest children served first?
Use your answers to the previous two problems to calculate the probability.
Hint:

Round to three places past the decimal if necessary.

Shaun orders a triple scoop cone with three different flavors. There are 31 flavors from which to choose.
How many different groups of flavors are possible?
First:
Is this a permutation or combination?
Why?

Shaun orders a triple scoop cone with three different flavors. There are 31 flavors from which to choose.
How many different groups of flavors are possible?

What formula would you use in the calculator?
Math, Prob, .... what do you choose?
Use the 'math keyboard' to enter the set up for either the permutation or combination,
use the box with a subscript on the far right to enter the numbers,
use the arrow key to get out of the subscript level.

Shaun orders a triple scoop cone with three different flavors. There are 31 flavors from which to choose.
How many different groups of flavors are possible?

Use your TI-84 calculator to find the answer. Use commas in your answer.
How many different groups of flavors are possible?

Shaun orders a triple scoop cone with three different flavors, but to choose his flavors he draws three slips of paper without looking from a jar containing a slip of paper for each flavor (31 of them).

How many different ways can the triple scoop cone contain two of his 5 favorite flavors & one non-favorite flavor?
Hint: this will involve two combination set ups, two of his 5 favorite flavors AND one non-favorite flavor
Use your TI-84 calculator to find the answer.
How many are possible?

Using the information from #21 and #20, what is the probability that the triple scoop cone contains two of his five favorite flavors?
Hint:

Round your decimal answer to three places past the decimal, then change to a percent.

A deck of cards is shuffled and dealt out completely to 4 players (13 cards each). How many different hands are possible for one player?
First:
Is this a permutation or combination?
Why?

A deck of 52 cards is shuffled and dealt out completely to 4 players (13 cards each). How many different hands are possible for one player?

Use your TI-84 to calculate the number of different hands possible. Remember the E tells you how many places to move your decimal.
Use commas when you enter your number (it's long).

While helping out at your little sister or brother's elementary classroom,the teacher asks you to take 3 students to the library. There are 24 students in the class. How many different groups could you take?

First:
Is this a permutation or combination?
Why?

While helping out at your little sister or brother's elementary classroom,the teacher asks you to take 3 students to the library. There are 24 students in the class. How many different groups could you take?

Use your TI-84 to calculate the number of different groups possible. Use commas when you enter your number.

The local Mal-mart store just received a shipment of 12 different bikes. From these, they will select 5 bikes to put on display in a line in front of the store. (they are lining up the bikes)
How many different lineups are possible?
First:
Is this a permutation or combination?
Why?

The local Mal-mart store just received a shipment of 12 different bikes. From these, they will select 5 bikes to put on display in a line in front of the store. (they are lining up the bikes)
How many different lineups are possible?

Use your TI-84 calculator to find the number of different lineups possible.
Use commas in your answer.

Using the 12 different bikes from the Mal-mart store, 9 of the 12 bikes in the shipment are motocross style.
Calculate the number of different lineups possible that have the first three bikes in the 5 bike lineup ARE motocross style and the next two ARE NOT.
use the # permutations possibles for the first 3 bikes are motocross AND the next two are not
Hint: first 3 ARE motocross style and the next 2 ARE NOT motocross style

Use the information from #28 & 29 to answer the question:
How likely is it (what is the probability) that exactly the first three bikes in the 5 bike lineup are motocross style?

Use:

Write your answer as a decimal rounded to the third place, or as a percent rounded to one place past the decimal.

Unit 8 Day 8 & 9 Sample Space & Probability Practice

A local restaurant offers a Prix Fixe menu, with a choice of an appertizer, an entree and a desert for one price.If there are 3 choices for the appetizer, 5 choices for the entree and 4 choices for dessert, how many different meals can be ordered?

Categorize the situations as involving a permutation or a combination:

A casino claims that its Roulette Wheel is truly random. What should that claim mean about the roulette wheel and its sections & colors?Explain below:

A doctor tells a patient just diagnosed with a serious disease that there's a 60% chance she'll live at least 5 years. Where do you think that probability comes from? (interpret this probability, remember our answers to the class kick from last week Thurs/Fri)

After an unusually dry autumn, a rado announcer is hear to say:'Watch out! We'll pay for these sunny days later on this winter.' Explain what he's trying to say and comment on the validity of his reasoning.Ex. what law is he using? Is his thinking flawed? Why?

You randomly choose 2 spices off a spice rack to complete your chili recipe.There are 20 spices on the rack. How many recipes are possible?First:Is this a permutation or combination?Why?

You randomly choose 2 spices off a spice rack to complete your chili recipe.There are 20 spices on the rack. How many recipes are possible?Use your TI-84 calculator to find the answer.How many different chili recipes are possible? (this is a sample space)

How many different ways can you choose two spices from the following list: cumin, red pepper, cinnamon, celery seed or thyme?First: What function will you use in the calculator? Enter it below with the math keyboard.

How many different ways can you choose two spices from the following list of 5 spices:cumin, red pepper, cinnamon, celery seed or thyme?Use your TI-84 to calculate the number of ways you can randomly choose the two spices from the group of 5.

The 5 Smith children run to the ice cream truck. In how many orders can they be served one at a time (they stand in line)First:Is this a permutation or combination?Why?

The 5 Smith children run to the ice cream truck. In how many orders can they be served one at a time (they stand in line)Use your TI-84 calculator to find the answer.How many different ways can the Smith children stand in line for ice cream? (this is a sample space)

What is the probability that the Smith children will line up with the two oldest children served first?Use your answers to the previous two problems to calculate the probability.Hint: Round to three places past the decimal if necessary.

Shaun orders a triple scoop cone with three different flavors. There are 31 flavors from which to choose.How many different groups of flavors are possible?First:Is this a permutation or combination?Why?

Shaun orders a triple scoop cone with three different flavors. There are 31 flavors from which to choose.How many different groups of flavors are possible?Use your TI-84 calculator to find the answer. Use commas in your answer.How many different groups of flavors are possible?

Using the information from #21 and #20, what is the probability that the triple scoop cone contains two of his five favorite flavors?Hint: Round your decimal answer to three places past the decimal, then change to a percent.

A deck of cards is shuffled and dealt out completely to 4 players (13 cards each). How many different hands are possible for one player?First:Is this a permutation or combination?Why?

While helping out at your little sister or brother's elementary classroom,the teacher asks you to take 3 students to the library. There are 24 students in the class. How many different groups could you take?First:Is this a permutation or combination?Why?

The local Mal-mart store just received a shipment of 12 different bikes. From these, they will select 5 bikes to put on display in a line in front of the store. (they are lining up the bikes)How many different lineups are possible?First:Is this a permutation or combination?Why?

Use the information from #28 & 29 to answer the question:How likely is it (what is the probability) that exactly the first three bikes in the 5 bike lineup are motocross style?Use: Write your answer as a decimal rounded to the third place, or as a percent rounded to one place past the decimal.

A local restaurant offers a Prix Fixe menu, with a choice of an appertizer, an entree and a desert for one price.
If there are 3 choices for the appetizer, 5 choices for the entree and 4 choices for dessert, how many different meals can be ordered?

A casino claims that its Roulette Wheel is truly random.
What should that claim mean about the roulette wheel and its sections & colors?

Explain below:

A doctor tells a patient just diagnosed with a serious disease that there's a 60% chance she'll live at least 5 years.
Where do you think that probability comes from?
(interpret this probability, remember our answers to the class kick from last week Thurs/Fri)

After an unusually dry autumn, a rado announcer is hear to say:
'Watch out! We'll pay for these sunny days later on this winter.'

Explain what he's trying to say and comment on the validity of his reasoning.
Ex. what law is he using? Is his thinking flawed? Why?

You randomly choose 2 spices off a spice rack to complete your chili recipe.
There are 20 spices on the rack. How many recipes are possible?
First:
Is this a permutation or combination?
Why?

You randomly choose 2 spices off a spice rack to complete your chili recipe.
There are 20 spices on the rack. How many recipes are possible?

Use your TI-84 calculator to find the answer.

How many different chili recipes are possible? (this is a sample space)

How many different ways can you choose two spices from the following list:
cumin, red pepper, cinnamon, celery seed or thyme?

First:
What function will you use in the calculator? Enter it below with the math keyboard.

How many different ways can you choose two spices from the following list of 5 spices:
cumin, red pepper, cinnamon, celery seed or thyme?

Use your TI-84 to calculate the number of ways you can randomly choose the two spices from the group of 5.

The 5 Smith children run to the ice cream truck. In how many orders can they be served one at a time (they stand in line)
First:
Is this a permutation or combination?
Why?

The 5 Smith children run to the ice cream truck. In how many orders can they be served one at a time (they stand in line)

Use your TI-84 calculator to find the answer.
How many different ways can the Smith children stand in line for ice cream? (this is a sample space)

What is the probability that the Smith children will line up with the two oldest children served first?
Use your answers to the previous two problems to calculate the probability.
Hint:

Round to three places past the decimal if necessary.

Shaun orders a triple scoop cone with three different flavors. There are 31 flavors from which to choose.
How many different groups of flavors are possible?
First:
Is this a permutation or combination?
Why?

Shaun orders a triple scoop cone with three different flavors. There are 31 flavors from which to choose.
How many different groups of flavors are possible?

Use your TI-84 calculator to find the answer. Use commas in your answer.
How many different groups of flavors are possible?

Using the information from #21 and #20, what is the probability that the triple scoop cone contains two of his five favorite flavors?
Hint:

Round your decimal answer to three places past the decimal, then change to a percent.

A deck of cards is shuffled and dealt out completely to 4 players (13 cards each). How many different hands are possible for one player?
First:
Is this a permutation or combination?
Why?

While helping out at your little sister or brother's elementary classroom,the teacher asks you to take 3 students to the library. There are 24 students in the class. How many different groups could you take?

First:
Is this a permutation or combination?
Why?

The local Mal-mart store just received a shipment of 12 different bikes. From these, they will select 5 bikes to put on display in a line in front of the store. (they are lining up the bikes)
How many different lineups are possible?
First:
Is this a permutation or combination?
Why?

Use the information from #28 & 29 to answer the question:
How likely is it (what is the probability) that exactly the first three bikes in the 5 bike lineup are motocross style?

Use:

Write your answer as a decimal rounded to the third place, or as a percent rounded to one place past the decimal.