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Quantitative Literacy
Probability

1
The Fundamental Counting Principle

Problem 1

A restaurant has \(3\) flavors of soda that come in \(3\) different cup sizes. How many different ways can you order a soda?

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Joshua
Joshua
Julieta
Julieta
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Julieta
Problem 2

Suppose you are taking a final exam that consists of \(8\) true-or-false questions. How many total possible ways can you answer the questions on your test?

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Logan
Logan
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Julieta
Problem 3

Consider the California area code 805. Theoretically, how many phone numbers are possible with this area code if the first digit following the area code cannot be zero or one? (Assume all combinations of numbers after the area code are allowed, except the aforementioned zero or one as the first digit.)

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Problem 4

Find the total possible outcomes for events \(A\) and \(B\).

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Joshua
Joshua
Julieta cc spanish language icon
Julieta

2
Permutations and Combinations

Problem 1

Find the number of permutations of the letters in the set \(\{\text{E, N, G, L, I, S, H}\}\).

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Joshua cc
Joshua
Stephanie cc
Stephanie
Julieta cc spanish language icon
Julieta
Problem 2

How many different ways are there to arrange the letters in the word CHEMISTRY?

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Logan cc
Logan
Stephanie cc
Stephanie
Julieta cc spanish language icon
Julieta
Problem 3

How many strings of letters can be made from the letters in the word FINAL, if no letter can be repeated?

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Mr. McKeague cc
Mr. McKeague
Logan cc
Logan
Julieta cc spanish language icon
Julieta
Problem 4

In how many ways can \(8\) people fill \(5\) chairs at a table?

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Joshua cc
Joshua
Stephanie cc
Stephanie
Julieta spanish language icon
Julieta
Problem 5

How many ways are there for three people from the set \(\{\text{Pat, Diane, Tim, JoAnn}\}\) to win first, second, and third prize in a contest?

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Julieta cc
Julieta
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Julieta
Problem 6

How many three-person committees can be formed from people in the set \(\{\text{Pat, Diane, Tim, JoAnn}\}\)?

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Mr. McKeague cc
Mr. McKeague
Stephanie cc
Stephanie
Julieta spanish language icon
Julieta
Problem 7

How many four-person committees can be selected from a set of \(7\) people?

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Mr. McKeague cc
Mr. McKeague
Stephanie cc
Stephanie
Julieta spanish language icon
Julieta
Problem 8

A jar contains \(4\) coins: a penny, a nickel, a dime, and a quarter. If \(2\) coins are selected, how many different amounts of money are possible?

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Mr. McKeague cc
Mr. McKeague
Stephanie cc
Stephanie
Julieta spanish language icon
Julieta

3
Introduction to Probability

Problem 1

Suppose you draw a card out of a \(52\)-card deck. You observe the color of the card in your hand. Give the sample space.

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Joshua cc
Joshua
Molly S. cc
Molly S.
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Cynthia
Problem 2

Inside a jar are six ping-pong balls, each showing numbers \(1\) through \(6\). Give the sample space of the ping-pong balls you can select.

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Joshua cc
Joshua
Molly S. cc
Molly S.
Cynthia spanish language icon
Cynthia
Problem 3

Inside a jar there are six ping-pong balls, each showing numbers \(1\) through \(6\). When you draw a ping-pong ball from the jar, what is the probability of drawing

  1. a ball with the number \(5\)?

  2. a ball with an odd number?

  3. a ball with a number other than \(5\)?

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Joshua cc
Joshua
Molly S. cc
Molly S.
Cynthia spanish language icon
Cynthia
Problem 4

Suppose you see five birds in a tree. Three of the birds are yellow and two are red. If one of them flew away, what is the probability that

  1. it is yellow?

  2. it is red?

  3. it is brown?

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Joshua cc
Joshua
Molly S. cc
Molly S.
Cynthia spanish language icon
Cynthia
Problem 5

Two \(6\)-sided dice are rolled at the same time and the numbers showing are observed. Find the following:

  1. The sample space

  2. \(P(\text{sum}=9)\)

  3. \(P(\text{sum}=11)\)

  4. \(P(\text{the sum is an odd number})\)

  5. \(P(\text{both dice show the same number})\)

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Joshua cc
Joshua
Molly S. cc
Molly S.
Cynthia spanish language icon
Cynthia
Problem 6

One card is drawn from a regular deck of \(52\) cards. Find the probabilities associated with the following events.

  1. The card is a \(5\).

  2. The card is a jack or a queen.

  3. The card is a spade.

  4. The card is not a \(5\).

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Julieta cc
Julieta
Joshua cc
Joshua
Molly S. cc
Molly S.
Cynthia spanish language icon
Cynthia
Problem 7

If an iPhone user was chosen at random, answer the following questions.

  1. What is the probability that they replaced another iPhone with their new iPhone?

  2. What is the probability that they replaced a Blackberry or an Android with their iPhone?

  3. What is the probability that they did not replace an old iPhone with their new iPhone?

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Joshua cc
Joshua
Molly S. cc
Molly S.
Cynthia spanish language icon
Cynthia
Problem 8

The table shows the length of time it took \(500\) college graduates to obtain their bachelor’s degree. If a graduate from this group is selected at random, find the probabilities of the following events. Give your answers as both reduced fractions and decimals rounded to the nearest hundredth.

  1. The graduate took \(4\) years to complete their degree.

  2. The graduate took more than \(6\) years or less than \(4\) years to complete their degree.

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Joshua cc
Joshua
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Cynthia

4
Probabilities and Compound Events

Problem 1
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Mrs. Diaz
Mrs. Diaz
Joshua
Joshua
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Julieta
Problem 2
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Mrs. Diaz
Mrs. Diaz
Logan
Logan
Julieta cc
Julieta
Problem 3
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Mrs. Diaz cc
Mrs. Diaz
Logan
Logan
Problem 4
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Mrs. Diaz cc
Mrs. Diaz
Joshua
Joshua

5
Mutually Exclusive Events and Their Probabilities

Problem 1
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Mrs. Diaz cc
Mrs. Diaz
Joshua
Joshua
Problem 2
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Mrs. Diaz cc
Mrs. Diaz
Logan
Logan

6
Conditional Probabilities: Independent and Dependent Events

Problem 1
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Mrs. Diaz cc
Mrs. Diaz
Joshua
Joshua
Problem 2
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Julieta cc
Julieta
Logan
Logan
Problem 3
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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta