Pre-Algebra

9-1 Probability

Warm UpWrite each fraction in simplest form.

1. 2. 3. 4.

Pre-Algebra

9-1 Probability

1620

1236

864

39195

45

13

18

15

Pre-Algebra

9-1 Probability

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

Pre-Algebra

9-1 ProbabilityVocabulary

experimenttrialoutcomesample spaceeventprobabilityimpossiblecertain

Pre-Algebra

9-1 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 Spaceflipping a coin heads, tailsrolling a number cube1, 2, 3, 4, 5, 6guessing the number of whole numbers jelly beans in a jar

Pre-Algebra

9-1 Probability

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.

Pre-Algebra

9-1 Probability

0 0.25 0.5 0.75 10% 25% 50% 75% 100%

Never Happens about Alwayshappens half the time happens

14

12

340 1

Pre-Algebra

9-1 Probability

Give the probability for each outcome.

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

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%.

Pre-Algebra

9-1 Probability

Give the probability for each outcome.

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

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) = .3

8

Pre-Algebra

9-1 ProbabilityExample 1B Continued

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

8Two 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. 3

838

28++ = 1

Pre-Algebra

9-1 Probability

Give the probability for each outcome.

Example 2A

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%.

Pre-Algebra

9-1 Probability

Give the probability for each outcome.

Example 2B

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 2 is P(2) = . 1

6

Pre-Algebra

9-1 ProbabilityExample 2B Continued

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

6One of the six sides of a cube is labeled 4, so a reasonable estimate of the probability that the spinner will land on 4 is P(4) = . 1

6One of the six sides of a cube is labeled 5, so a reasonable estimate of the probability that the spinner will land on 5 is P(5) = . 1

6

Pre-Algebra

9-1 ProbabilityExample 2B 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 6 is P(6) = . 1

6Check The probabilities of all the outcomes must add to 1.

16

16

16++ = 11

6+ 16+ 1

6+

Pre-Algebra

9-1 Probability

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