Pre-Algebra

Probability

9.1

Write each fraction in simplest form.

1. 2.

3. 4.

1620

1236

864

39195

4

5

1

3

1

8

1

5

Warm Up

Learn to find the probability of an event by using the definition of probability.

experimenttrialoutcomesample spaceeventprobabilityimpossiblecertain

Vocabulary

An experiment is an activity in which results are observed. Each observation is called a trial, and each result is called an outcome. The sample space is the set of all possible outcomes of an experiment.

Experiment Sample Space

flipping a coin heads, tails

rolling a number cube 1, 2, 3, 4, 5, 6

guessing the number of whole numbers jelly beans in a jar

An event is any set of one or more outcomes. The probability of an event, written P(event), is a number from 0 (or 0%) to 1 (or 100%) that tells you how likely the event is to happen.

• A probability of 0 means the event is impossible, or can never happen.

• A probability of 1 means the event is certain, or has to happen.

• The probabilities of all the outcomes in the sample space add up to 1.

0 0.25 0.5 0.75 1

0% 25% 50% 75% 100%

14

12

340 1

Never Happens about Alwayshappens half the time happens

Give the probability for each outcome.

A. The basketball team has a 70% chance of winning.

The probability of winning is P(win) = 70% = 0.7. The probabilities must add to 1, so the probability of not winning is P(lose) = 1 – 0.7 = 0.3, or 30%.

Example: Finding Probabilities of Outcomes in a Sample Space

Give the probability for each outcome.

B.

Three of the eight sections of the spinner are labeled 1, so a reasonable estimate of the probability that the spinner will land on 1 is

P(1) = .38

Example: Finding Probabilities of Outcomes in a Sample Space

Three of the eight sections of the spinner are labeled 2, so a reasonable estimate of the probability that the spinner will land on 2 is P(2) = .3

8

Two of the eight sections of the spinner are labeled 3, so a reasonable estimate of the probability that the spinner will land on 3 is P(3) = = .2

814

Check The probabilities of all the outcomes must add to 1.

38

38

28

++ = 1

Example Continued

Give the probability for each outcome.

A. The polo team has a 50% chance of winning.

The probability of winning is P(win) = 50% = 0.5. The probabilities must add to 1, so the probability of not winning is P(lose) = 1 – 0.5 = 0.5, or 50%.

Try This

Give the probability for each outcome.

B. Rolling a number cube.

One of the six sides of a cube is labeled 1, so a reasonable estimate of the probability that the spinner will land on 1 is P(1) = . 1

6

Outcome 1 2 3 4 5 6

Probability

One of the six sides of a cube is labeled 2, so a reasonable estimate of the probability that the spinner will land on 1 is P(2) = . 1

6

Try This

One of the six sides of a cube is labeled 3, so a reasonable estimate of the probability that the spinner will land on 1 is P(3) = . 1

6

One of the six sides of a cube is labeled 4, so a reasonable estimate of the probability that the spinner will land on 1 is P(4) = . 1

6

One of the six sides of a cube is labeled 5, so a reasonable estimate of the probability that the spinner will land on 1 is P(5) = . 1

6

Try This Continued

One of the six sides of a cube is labeled 6, so a reasonable estimate of the probability that the spinner will land on 1 is P(6) = . 1

6

Check The probabilities of all the outcomes must add to 1.

16

16

16

++ = 116

+16

+16

+

Try This Continued

To find the probability of an event, add the probabilities of all the outcomes included in the event.

A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.

A. What is the probability of not guessing 3 or more correct?

The event “not three or more correct” consists of the outcomes 0, 1, and 2.

P(not 3 or more) = 0.031 + 0.156 + 0.313 = 0.5, or 50%.

Example: Finding Probabilities of Events

A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.

B. What is the probability of guessing between 2 and 5?

The event “between 2 and 5” consists of the outcomes 3 and 4.

P(between 2 and 5) = 0.313 + 0.156 = 0.469, or 46.9%

Example: Finding Probabilities of Events

A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.

C. What is the probability of guessing an even number of questions correctly (not counting zero)?The event “even number correct” consists of the outcomes 2 and 4.

P(even number correct) = 0.313 + 0.156 = 0.469, or 46.9%

Example: Finding Probabilities of Events

A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.

A. What is the probability of guessing 3 or more correct?

The event “three or more correct” consists of the outcomes 3, 4, and 5.

P(3 or more) = 0.313 + 0.156 + 0.031 = 0.5, or 50%.

Try This

A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.

B. What is the probability of guessing fewer than 3 correct?

The event “fewer than 3” consists of the outcomes 0, 1, and 2.

P(fewer than 3) = 0.031 + 0.156 + 0.313 = 0.5, or 50%

Try This

A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.

C. What is the probability of passing the quiz (getting 4 or 5 correct) by guessing?

The event “passing the quiz” consists of the outcomes 4 and 5.

P(passing the quiz) = 0.156 + 0.031 = 0.187, or 18.7%

Try This

Use the table to find the probability of each event.

1. 1 or 2 occurring

2. 3 not occurring

3. 2, 3, or 4 occurring0.874

0.351

0.794

Lesson Quiz