## Coin and Number Cube

## Opening

# Coin and Number Cube

Suppose you toss a coin and roll a six-sided number cube.

- What is the theoretical probability that you will get heads and a 3?

Suppose you toss a coin and roll a six-sided number cube.

- What is the theoretical probability that you will get heads and a 3?

Explore compound independent events by calculating and comparing expected and experimental results.

If you toss 3 coins, what is the probability that you will toss 1 heads and 2 tails?

- Create a diagram showing the sample space.
- Find the theoretical probability of the event.
- Predict the results for 100 trials.
- Perform 100 trials.
- How do your expected results compare to your experimental results?

INTERACTIVE: Three Coins

If you spin 2 four-part spinners (each with the same, equal-sized sections and colors), what is the probability that you will spin matching colors?

- Create a diagram showing the sample space.
- Find the theoretical probability of the event.
- Predict the results for 100 trials.
- Perform 100 trials.
- How do your expected results compare to your experimental results?

INTERACTIVE: Two Spinners

- Summarize your work for both problems: Show the sample space, provide the theoretical probability that you calculated, and explain your experimental results.
- Discuss your comparison of the theoretical probability and experimental results, justifying any conclusions you make with your work.

- Create a problem for your partner to solve that requires finding the probability of two compound independent events.
- Exchange problems with your partner and together reach an agreement for the answers to both problems.

Take notes about how your classmates' expected results compare to their experimental results.

As your classmates present, ask questions such as:

- How did you find the sample space and the number of favorable outcomes?
- Can you explain what your diagram of the sample space tells us?
- How did you decide what the expected results would be?
- How do your results for 100 trials compare with your expected results?
- Why do you think your expected results and experimental results compare in this way?
- How do your results for 100 trials compare to the class results?
- Which results—your results or the class results—are closer to the theoretical probability? Explain.

**Read and Discuss**

*Multistage experiments* result in *compound events*. Compound events are are composed of *independent events* if the occurrence of one event does not affect the outcome of the other event—that is, if the probability of one event is unrelated to the probability of the other event.

The *sample space* of a multistage experiment is the set of all possible outcomes of that experiment. You can represent the sample space of a multistage experiment using tree diagrams, lists, and tables, and use these representations to find the probability of compound events.

If you simulate a multistage experiment, the larger the sample size you use, the closer your experimental results will be to the expected results (the theoretical probability).

Can you:

- Define
*independent events*? - Explain how you can use representations of the sample space to find the probability of compound events?
- Explain the difference between expected results (theoretical probability) and experimental results?
- Explain how sample size affects experimental results?

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**Something I still do not understand about probability is...**