Holt CA Course 1

11-5 Probability

Warm UpWarm Up

California StandardsCalifornia Standards

Lesson Presentation

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Holt CA Course 1

11-5 Probability

Warm UpWrite each fraction in simplest form.

1. 2.

3. 4.

1620

1236

864

39195

4

5

1

3

1

8

1

5

Holt CA Course 1

11-5 Probability

Review of Grade 6 SDAP3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1 – P is the probability of an event not occurring.

California Standards

Holt CA Course 1

11-5 Probability

Vocabulary

experimenttrialoutcomesample spaceeventprobability

Holt CA Course 1

11-5 Probability

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

Holt CA Course 1

11-5 Probability

An event is any set of one or more outcomes. The probability of an event is a number from 0 (or 0%) to 1 (or 100%) that tells you how likely the event is to happen. You can write probability as a fraction, a decimal, or a percent.

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

• A probability of 1 means the event is certain, or will always happen.

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

Holt CA Course 1

11-5 Probability

0 0.25 0.5 0.75 1

0% 25% 50% 75% 100%

Never Happens about Alwayshappens half the time happens

14

12

340 1

Holt CA Course 1

11-5 Probability

Give the probability for each outcome.

Additional Example 1A: Finding Probabilities of Outcomes in a Sample Space

The basketball team has a 70% chance of winning.

P(win) = 70% = 0.7.

P(lose) = 1 – 0.7 = 0.3, or 30%

Holt CA Course 1

11-5 Probability

Give the probability for each outcome.

Additional Example 1B: Finding Probabilities of Outcomes in a Sample Space

Three of the eight sections of the

spinner are labeled 1, so is a

reasonable estimate.

P(1) = 38

3 8

Holt CA Course 1

11-5 ProbabilityAdditional Example 1B Continued

P(2) =38

Check The probabilities of all the outcomes must add to 1. 3

838

28

++ = 1

Three of the eight sections of the

spinner are labeled 2, so is a

reasonable estimate.

3 8

P(3) =28

Two of the eight sections of the

spinner are labeled 3, so is a

reasonable estimate.

2 8

Holt CA Course 1

11-5 Probability

Give the probability for each outcome.

Check It Out! Example 1A

The polo team has a 50% chance of winning.

P(win) = 50% = 0.5.

P(lose) = 1 – 0.5 = 0.5, or 50%.

Holt CA Course 1

11-5 Probability

Give the probability for each outcome.

Check It Out! Example 1B

Three of the eight sections of the

spinner are teal, so is a

reasonable estimate.

P(teal) = 38

3 8

Outcome Teal Red Orange

Probability

Holt CA Course 1

11-5 ProbabilityCheck It Out! Example 1B Continued

P(red) =38

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

38

38

28

++ = 1

P(orange) =28

Three of the eight sections of the

spinner are red, so is a

reasonable estimate.

3 8

Two of the eight sections of the

spinner are orange, so is a

reasonable estimate.

2 8

Holt CA Course 1

11-5 Probability

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

Holt CA Course 1

11-5 Probability

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

Additional Example 2A: Finding Probabilities of Events

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 correct) = 0.313 + 0.156 + 0.031 = 0.5, or 50%.

Holt CA Course 1

11-5 Probability

What is the probability of guessing fewer than 2 correct?

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

P(fewer than 2 correct) = 0.031 + 0.156 = 0.187, or 18.7%.

Additional Example 2B: Finding Probabilities of Events

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

Holt CA Course 1

11-5 Probability

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

Check It Out! Example 2A

What is the probability of guessing 2 or more correct?

The event “two or more correct” consists of the outcomes 2, 3, 4, and 5.

P(2 or more) = 0.313 + 0.313 + 0.156 + 0.031 = 0.813, or 81.3%.

Holt CA Course 1

11-5 Probability

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%.

Check It Out! Example 2BA quiz contains 5 true-false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.

Holt CA Course 1

11-5 Probability

Lesson Quiz

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