Lesson 32

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​Theoretical Probability

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Recap and Vocabulary and Examples

• ​The theoretical probability of an event occurring is what you would expect to happen in an experiment.

  • For example, you expect a tossed coin to land heads up half the time. So, the theoretical probability of a coin landing heads up is 50%.

• We already learned about experimental probability, which lets you use the results from past experiments to predict the results of future experiments.

REMEMBER:
The experimental probability of an event is not always the same as the theoretical probability. You might use experimental probability, theoretical probability, or both to make a prediction.

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Vocabulary

Math Vocabulary

• sample space: the set of all possible unique outcomes for an experiment.

• theoretical probability: the probability of an event occurring based on what is expected to happen.

• event: a set of one or more outcomes of an experiment.

• experimental probability: the probability of an event occurring based on the results from an experiment.

• outcome: one of the possible results of a chance experiment.

Academic Vocabulary

• favorable: of interest or being studied.

• nonfavorable: not of interest or not being studied.

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Explore Theoretical Probability

Each of the 10 letters in the word BIENVENIDO is written on a separate slip of paper and placed in a bag. Each of the 5 letters in the word ADIOS is written on a separate slip of paper and placed in another bag. Khadija plans to select a letter at random from each bag. She thinks she is equally likely to select a letter D from each bag.

Discuss why you agree or disagree.

Open Ended

Each of the 10 letters in the word BIENVENIDO is written on a separate slip of paper and placed in a bag. Each of the 5 letters in the word ADIOS is written on a separate slip of paper and placed in another bag. Khadija plans to select a letter at random from each bag. She thinks she is equally likely to select a letter D from each bag.

Show why you agree or disagree.

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Look Ahead

1. When you find the probability of an event based on results from an experiment, you are finding the experimental probability of that event.

2. The theoretical probability of an event is found by analyzing the possible outcomes, rather than by conducting an experiment.

Consider the spinners below. The sections on Spinner 1 are all the same size. Sections B and Con Spinner 2 are the same size. All sections on Spinner 3 are the same size.

Multiple Choice

The sample space for an experiment is the set of all possible unique outcomes.

For all of these spinners, the sample space is the same. What is the sample space for the spinners?

• ABC

• AABC

• ABCC

• ABCD

Open Ended

Sometimes all of the outcomes of an experiment are equally likely. Other times, all outcomes are not equally likely. Explain why the outcomes for Spinner 1 are equally likely but the outcomes for Spinner 2 are not.

Open Ended

(Please copy words in orange) When outcomes are equally likely, you can find the theoretical probability of an event using the fraction $$\frac{number\ of\ favorable\ outcomes}{total\ number\ of\ outcomes}$$ . What is the probability of spinning an A on Spinner 1?

Open Ended

For Spinner 3, the outcomes are not equally likely. To find the probability of spinning a C, consider what fraction of the spinner consists of the favorable outcome C. What is the probability of spinning a C on Spinner 3?

Open Ended

Each of the seven letters in the word WELCOME is written on a separate slip of paper and placed in Box 1. Each of the seven letters in the word GOODBYE is written on a separate slip of paper and placed in Box 2. Jayden plans to select a letter at random from each box. He thinks he is equally likely to select a letter O from each box. Show why Jayden is correct or incorrect. Show me another way.

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