Example 1 Find Probability

Example 2 Find Probability

Example 3 Use Probability to Solve a Problem

There are six equally likely outcomes on the spinner shown. Find the probability of spinning a 1.

Find the probability of spinning a 1.

Answer: The probability of spinning a 1 is

A number cube is rolled. Find the probability of rolling a 4.

Answer:

There are six equally likely outcomes on the spinner shown. Find the probability of spinning a 2 or a 4.

Simplify.

Answer: The probability of spinning a 2 or a 4 is

A number cube is rolled. Find the probability of rolling a number greater than 3.

Answer:

SPORTS A sportscaster predicted that the Tigers had a 75% chance of winning tonight. What is the probability that the Tigers will not win?The two events are complementary. So, the sum of the probabilities is 1.

Replace with 0.75.

Subtract 0.75 from each side.

Answer: So, the probability that the Tigers will not win tonight is 0.25 or 25%.

SLEEPOVER Celia guesses that the probability that her parents will allow her to sleep over at her best friend’s house tonight is 55%. What is the probability that Celia will not be allowed to sleep over?

Answer: 0.45 or 45%

Example 1 Find a Sample Space

Example 2 Use a Tree Diagram to Find Probability

Example 3 Use a List to Find Sample Space

A car can be purchased with either two doors or four doors. You may also choose leather, fabric, or vinyl seats. Draw a tree diagram that shows all the buying options.

Use a tree diagram. List each choice for the number of doors. Then pair each choice for the number of doors with each choice for the type of seats.

Answer:

There are 6 possible buying options.

A pair of sneakers can be purchased with either laces or Velcro. You may also choose white, gray, or black sneakers. Draw a tree diagram that shows all the different sneakers possible.

Answer:

There are 6 possible sneakers.

Marisa rolls two number cubes. What is the probability that she will roll a five on the first cube and a 2 on the second cube?

Use a tree diagram to find all of the possible outcomes.

One outcome has a 5 on the first cube and a 2 on the second cube. There are 36 possible outcomes.

Answer:

Max rolls two number cubes. What is the probability that he will roll two numbers whose sum is 9?

Answer:

VACATION SPOTS The names of four vacation spots are listed below. In how many ways can you choose two of the four spots?

Vacation Spots

Seaside Hotel

Mountain View Lodge

Island Paradise

Canyon Cabin

List all of the ways two vacation spots can be chosen.

SM SI SC

MS MI MC

IS IM IC

CS CM CIFrom the list count only the different arrangements. In this case, SM is the same as MS.

SM SI SC

MI MC IC

Answer: There are 6 possible ways to choose two of the four vacation spots.

STUDENT COUNCIL Steven, Betsy, Sally, David, and Ken all want to represent their class on the student council. In how many ways can two of the five students be chosen for student council?

Answer: 10 possible ways

Example 1 Determine a Good Sample

Example 2 Make Predictions Using Proportions

Example 3 Make Predictions Using Proportions

Every fifth person entering a school gymnasium for a community meeting is asked to name his or her favorite clothing store at either of two nearby malls. Determine whether the sample is a good sample.

Asking every fifth person ensures a random survey.

The sample should be representative of the larger population; that is, every person living in the community.

The sample is large enough to provide accurate information.

Answer: So, this sample is a good sample.

Every fourth family listed in a school’s phone directory is called and asked their opinion on the upcoming vote for school board members. Determine whether the sample is a good sample.

Answer: The sample is good because asking every fourth family ensures a random survey, the sample is large enough to provide accurate information, and the topic is an unbiased one for the setting.

RECREATION Julia asked every sixth person in the school cafeteria to name the kind of activity he or she would like to have for the school’s spring outing. What is the probability that a student will prefer an amusement park?

Spring Outing

Outing Students

amusement park 15

baseball game 10

water park 10

art museum 5

number of students that prefer an amusement park

number of students surveyed

Answer:

HOCKEY Kyle asked every third hockey player in his league what type of snack they prefer to have after a hockey game. What is the probability that a hockey player will prefer cookies for their snack?

Post Game Snack

Snack Students

fruit 12

chips 18

cookies 10

Answer:

RECREATION Julia asked every sixth person in the school cafeteria to name the kind of activity he or she would like to have for the school’s spring outing. There are 408 students at the school Julia attends. Predict how many students prefer going to an amusement park.

Spring Outing

Outing Students

amusement park 15

baseball game 10

water park 10

art museum 5

Use a proportion.

Write the proportion.

Write the cross products.

Multiply.

Divide each side by 40.

Answer: Of the 408 students, about 153 will prefer going to an amusement park.

Let a students who prefer an amusement park.

HOCKEY Kyle asked every third hockey player in his league what type of snack they prefer to have after a hockey game. There are 128 hockey players in Kyle’s league. Predict how many of the hockey players prefer cookies for their snack after a game.

Post Game Snack

Snack Students

fruit 12

chips 18

cookies 10

Answer: 32

Example 1 Find Probability Using Area Models

Example 2 Use Probability to Make Predictions

Example 3 Use Probability to Make Predictions

Find the probability that a randomly thrown dart will land in the shaded region of the dartboard to the right.

Answer: So, the probability is

Find the probability that a randomly thrown dart will land in the shaded region of the dartboard below.

Answer:

COMMUNICATION Romeo tries to get Juliet’s attention by tossing pebbles at her window that is shown below. Find the probability that the pebble will land in Region B. Assume it is equally likely for a pebble to hit anywhere on the window.

Area of Region B Area of Window

Answer: So, the probability that a pebble will land in

Region B is

GAMES A carnival game is played by throwing bean bags at a board. If a bean bag hits one of the shaded squares, the player wins a prize. Find the probability that a player will win.

Answer:

COMMUNICATION Romeo tries to get Juliet’s attention by tossing pebbles at her window that is shown below. Predict how many times a pebble will land in Region B if Romeo throws 300 pebbles one at a time.

Write the cross products.

Multiply.

Divide each side by 6.

Write a proportion that compares the number of pebbles landing in region B to the number of pebbles thrown. Let the number of pebbles landing in Region B.

pebbles landing in Region B pebbles thrown

Answer: About 50 of the pebbles will land in Region B.

GAMES A carnival game is played by throwing bean bags at a board. If a bean bag hits one of the shaded squares, the player wins a prize. Predict how many times a player will win the game if they play 60 times.

Answer: about 20 times

Example 1 Find Probability of Independent Events

Example 2 Find Probability of Independent Events

A number cube is rolled and a coin is tossed. Find the probability of rolling a 2 and landing on heads.

Answer: So, the probability is

A number cube is rolled and the spinner is spun. Find the probability of rolling an even number and spinning a 4.

Answer:

GRID-IN TEST ITEM To win the grand prize, Ted has to choose one of 10 keys to match with one of 3 treasure chests. What are Ted’s chances of winning?

Solve the Test Item

Read the Test ItemTo find the probability,

Answer:

GRID-IN TEST ITEM Sarah placed 4 yellow chips and 8 pink chips into a bag. She selected 1 chip without looking, replaced it, and then selected a second chip. Find the probability that she first selected a yellow chip and then selected a pink chip.

Answer: