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# Theoretical and Experimental Coin Tosses

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# Theoretical and Experimental Probability - Answer Key

## Basketball and Theoretical and Experimental Probability

### Topic

Basketball and Theoretical and Experimental Probability

### Vocabulary

• Theoretical Probability
• Experimental Probability

### Student Exploration

#### What is the theoretical and experimental probability that you will make a 3-point basket in basketball? And how are they different?

A basketball hoop.

What is the difference between theoretical and experimental probability? This is an activity where you can explore the difference between theoretical and experimental probability. You just learned that theoretical probability is a ratio expressing the number of successful outcomes compared to the total outcomes in an experiment. Right now, make an estimate of the theoretical probability of you making a 3-pointer in basketball. A 3-pointer is a field goal shot made in a basketball game beyond the 3-point arc on a basketball court.

In order to determine your theoretical probability of making a 3-pointer in basketball, estimate how many 3-point shots you would accurately make out of 10 shots. Then set up that ratio as a fraction, and reduce it.

1. What is the theoretical probability of you making a 3-pointer? Show your work.
Answers will vary and this is just an example of answers. My theoretical probability of making a 3-pointer in basketball is $\frac{3}{10}$ (which cannot be reduced).

Now go find the basketball court that is closest to you! Go outside to that basketball court and shot ten 3-pointer shots (shots beyond the 3-point arc) and record how many baskets you make. This is your experimental probability! Set up a ratio of the number of 3-point shots that you made compared to 10, the total number of trails in your experiment. Set up that ratio as a fraction, and reduce it.

2. What is the experimental probability of you making a 3-pointer? Show your work.
My experimental probability of making a 3-pointer is $\frac{4}{10} = \frac{2}{5}$.
3. Compare your theoretical and experimental probability of making a 3-pointer. How are they different? How are they similar? Explain.
My theoretical and experimental probabilities are very similar as my theoretical probability was $\frac{3}{10}$ and my experimental probability was $\frac{2}{5}$. They are only different by $\frac{1}{10} = 0.1$.
4. If you were to compare this same experiment but take 20 shots, how would your results change? Explain.
If I did the same experiment but took 20 shots the fraction won’t necessarily change as the fraction represents a ratio of the shots that you make compared to the 20 shots that you took. However if you are not a regular basketball player you might get tired when taking 20 shots and your accuracy might lessen as you continue, causing the experimental probability of you making a shot to go down (the fraction to get smaller and closer to zero).

A basketball player.

5. Now, compare your experimental probability to that of your favorite basketball player at the website below. If you don’t know any famous basketball players check out Kevin Durant and Lebron James, these were two of the top players in the 2012 NBA play-offs. Explain what you find.

### Extension Investigation

These are some follow-up questions to the activity above.

1. Does experimental probability get closer or further away from the theoretical probability as you do more trails? Explain. As more experiments are conducted the experimental probability should get closer to the theoretical probability. Although there will be some outliers, the majority of the experiment data will be closely aligned to the theoretical probability.
2. What can you infer about a situation when the experimental probability is very different from the theoretical probability? Explain. If the experimental probability is very different from the theoretical probability two explanations as to why are as follows. The first explanation is that not enough experiments have been conducted and with more experiments the experimental probability will began to approach the theoretical probability. A second explanation is that the theoretical probability is incorrect and needs to be recalculated.

### Connections to other CK-12 Subject Areas

• Probability and Permutations
• Theoretical and Experimental Spinners
• Theoretical and Experimental Coin Tosses

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