9-1 Probability

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

9-1 Probability

Warm UpWrite each fraction in simplest form.

1. 15 212. 48 643. 9 814. 30 45

57341923

9-1 Probability

Problem of the Day

You roll a regular pair of number cubes. How likely is it that the product of the two numbers is odd and greater than 25? Explain.

Impossible; the only possible products greater than 25 (30 and 36) are even.

9-1 Probability

MA.7.P.7.1 Determine the outcome of an experiment and predict which events are likely or unlikely.

Sunshine State Standards

9-1 Probability

Vocabulary

experiment complementtrialoutcomeeventprobabilitysimple eventcompound event

9-1 Probability

An activity involving chance, such as rolling a cube, is called an experiment. Each repetition or observation of an experiment is a trial, and each result is an outcome. A set of one or more outcomes is an event. For example, rolling a 5 (one outcome) can be an event, or rolling an even number (more than one outcome) can be an event.

9-1 Probability

The probability of an event, written P(event), is the measure of how likely an event is to occur. A simple event has a single outcome. A compound event is two or more simple events. Probability is a measure between 0 and 1, as shown on the number line. You can write probability as a fraction, a decimal, or a percent.

9-1 Probability

Determine whether each event is impossible, unlikely, as likely as not, likely, or certain.

Additional Example 1A: Determining the Likelihood of an Event

rolling an odd number on a number cube

There are 6 possible outcomes:

2, 4, 61, 3, 5

Not OddOdd Half of the outcomes are odd.

Rolling an odd number is as likely as not.

9-1 Probability

Determine whether each event is impossible, unlikely, as likely as not, likely, or certain.

Additional Example 1B: Determining the Likelihood of an Event

rolling a number less than 6 on a number cube

There are 6 possible outcomes:

61, 2, 3, 4, 5

6 or moreLess than 6 Five outcomes are less than 6.

Rolling a number less than 6 is likely.

9-1 Probability

Determine whether each event is impossible, unlikely, as likely as not, or certain.

Check It Out: Example 1A

rolling a 2 on a number cube

unlikely

rolling a 7 on a number cube

impossible

1A

1B

9-1 Probability

When a number cube is rolled, either a 5 will be rolled or it will not. Rolling a 5 and not rolling a 5 are examples of complementary events. The complement of an event is the set of all outcomes that are not the event.

Because it is certain that either an event or its complement will occur when an activity is performed, the sum of the probabilities is 1.

P(event) + P(complement) = 1

9-1 Probability

Additional Example 2: Using Complements

A bag contains circular chips that are the same size and weight. There are 8 purple, 4 pink, 8 white, and 2 blue chips in the bag. The

probability of drawing a pink chip is . What

is the probability of not drawing a pink chip?

2 11

P(event) + P(complement) = 1

9-1 Probability

Additional Example 2 Continued

P(event) + P(complement) = 1

P(pink) + P(not pink) = 1

+ P(not pink) = 12 11

Substitute for P(pink).2 11

2 11

- = - 2 11

P(not pink) = 9 11

Subtract from both t sides.

2 11

Simplify

The probability of not drawing a pink chip is . 9 11

9-1 Probability

Check It Out: Example 2

A bag contains 7 red marbles, 3 green marbles, and 2 yellow marbles. The probability of drawing a red or green marble is . What is the probability of drawing a yellowmarble?

5 6

P (event) + P (complement) = 1

P (yellow) + P (red or green) = 1

P (yellow) + 56 = 1

P (yellow) = 1- 56

=16

9-1 Probability

Mandy’s science teacher almost always introduces a new chapter by conducting an experiment. Mandy’s class finished a chapter on Friday. Should Mandy expect the teacher to conduct an experiment next week? Explain.

Additional Example 3: School Application

Since the class will be starting a new chapter, it is likely the teacher will conduct an experiment.

9-1 Probability

Check It Out: Example 3A

Bethany rarely gets home before 5 p.m. when she has band practice after school. If Bethany has band practice on Thursday, would you expect her to be home at 4 p.m. that day? Explain.

If Bethany has band practice on Thursday, it’s unlikely that she would be at home at 4 P.M

9-1 Probability

Check It Out: Example 3B

Terence usually buys new mp3s the day after he gets his allowance. If he got his allowance on Friday, would you expect him to buy new mp3s on Saturday? Explain.

If Terence gets his allowance on Friday, it’s likely he would buy mp3s on Saturday.

9-1 Probability

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

9-1 Probability

Lesson Quiz: Part I

Determine whether each event is impossible, unlikely, as likely as not, likely, or certain.

1. Bonnie’s Spanish club meets on Tuesday afternoons. How likely is it that Bonnie is at the mall on Tuesday afternoon?

2. There are 12 SUVs and 12 vans in a parking lot. How likely is it that the next vehicle to move is a van?

unlikely

as likely as not

9-1 Probability

Lesson Quiz: Part IIDetermine whether each event is impossible, unlikely, as likely as not, likely, or certain.

3. A bag holds 4 red marbles, 3 green marbles, 3 yellow marbles, and 2 blue marbles. You pull one without looking. The probability of pulling a green marble is . What is the probability of pulling a marble that is not green?3 4

4. Tim never listens to his MP3 player during classes. If Tim is in math class, how likely is it that he is listening to his MP3 player?impossible

14

9-1 Probability

1. Determine whether the event is impossible, unlikely, likely, or certain.

rolling a 7 on a number cube

A. impossible

B. unlikely

C. likely

D. certain

Lesson Quiz for Student Response Systems

9-1 Probability

2. Determine whether the event is unlikely, as likely as not, likely, or certain.

randomly drawing a black or white marble from a bag of black and white marbles

A. impossible

B. unlikely

C. likely

D. certain

Lesson Quiz for Student Response Systems

9-1 Probability

3. Erika almost always goes out with an umbrella if it is a rainy day. Today is a rainy day. How likely is it that Erika will go out with umbrella today?

A. impossible

B. unlikely

C. likely

D. certain

Lesson Quiz for Student Response Systems