12-4 theoretical probability course 1 warm up warm up lesson presentation lesson presentation...

12-4 Theoretical Probability

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpA café offers a soup-and-sandwich combination lunch. You can choose tomato soup, chicken noodle soup, or clam chowder. You can choose a turkey, ham, veggie, or tuna sandwich. How many lunch combinations are there?12

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Problem of the Day

Rory dropped a quarter, a nickel, a dime, and a penny. What is the probability that all four landed tails up?

116__

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Learn to find the theoretical probability and complement of an event.

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Vocabulary

theoretical probabilityequally likelyfaircomplement

Insert Lesson Title Here

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Another way to estimate probability of an event is to use theoretical probability. One situation in which you can use theoretical probability is when all outcomes have the same chance of occurring. In other words, the outcomes are equally likely.

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An experiment with equally likely outcomes is said to be fair. You can usually assume that experiments involving items such as coins and number cubes are fair.

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Additional Example 1A: Finding Theoretical Probability

What is the probability of this fair spinner landing on 3?

There are three possible outcomes when spinning this spinner: 1, 2, or 3. All are equally likely because the spinner is fair.

P(3)= 3 possible outcomes _________________

There is only one way for the spinner to land on 3.

P(3)= 3 possible outcomes __________________1 way event can occur

=1

3__

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Additional Example 1B: Finding Theoretical Probability

What is the probability of rolling a number greater than 4 on a fair number cube?

There are six possible outcomes when a fair number cube is rolled: 1, 2, 3, 4, 5, or 6. All are equally likely. There are 2 ways to roll a number greater than 4:5 or 6.

P(greater than 4)= 6 possible outcomes _________________

P(greater than 4)= 6 possible outcomes ____________________2 ways events can occur

=1

3__

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Check It Out: Example 1A

What is the probability of this fair spinner landing on 1 or 2?

There are three possible outcomes when spinning this spinner: 1, 2, or 3. All are equally likely because the spinner is fair.

P(3)= 3 possible outcomes _________________

There are two ways for the spinner to land on 1 or 2.

P(3)= 3 possible outcomes __________________2 ways event can occur

=2

3__

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Check It Out: Example 1B

What is the probability of rolling a number less than 4 on a fair number cube?

There are six possible outcomes when a fair number cube is rolled: 1, 2, 3, 4, 5, or 6. All are equally likely. There are 3 ways to roll a number greater than 4:3, 2 or 1.

P(less than 4)= 6 possible outcomes _________________

P(less than 4)= 6 possible outcomes ____________________3 ways events can occur

=12__

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When you combine all the ways that an event can NOT happen, you have the complement of the event.

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Additional Example 2: Finding the Complement of an Event

Suppose there is a 45% chance of snow tomorrow. What is the probability that it will not snow?

In this situation there are two possible outcomes, either it will snow or it will not snow.

P(snow) + P(not snow) = 100%

45% + P(not snow) = 100%

-45% -45%

P(not snow) = 55%

_____ _____ Subtract 45% from each side.

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Check It Out: Example 2

Suppose there is a 35% chance of rain tomorrow. What is the probability that it will not rain?

In this situation there are two possible outcomes, either it will rain or it will not rain.

P(rain) + P(not rain) = 100%

35% + P(not rain) = 100%

P(not rain) = 65%

-35% -35% _____ _____ Subtract 35% from each side.

Lesson Quiz

Use the spinner shown for problems 1-3.

1. P(2)

2. P(odd number)

3. P(factor of 6)

4. Suppose there is a 2% chance of spinning the

winning number at a carnival game. What is

the probability of not winning?

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98%

2

7__

4

7__

4

7__

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12-4 theoretical probability course 1 warm up warm up lesson presentation lesson presentation...

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