It’s known that a certain basketball player makes 30% of his free throws. On Friday night’s game, he had the chance to shoot 10 free throws. How many free throws might you expect him to make? We would expect 0.30 * 10 = 3.

However, he actually made 4 free throws out of 10 or 40%. Is this surprising? Does this mean that he’s actually better than we thought?

The *binomial distribution* can help us. It tells us how likely it is for a certain number of “successes” to happen, given a probability of success and a number of trials.

In this example:

- The
*probability of success*was 30% (he makes 30% of free throws) - The number of
*trials*was 10 (he took 10 shots) - The number of
*successes*was 4 (he made 4 shots)

The binomial distribution is important because it allows us to know how likely a certain outcome is, even when it’s not the expected one. From this graph, we can see that it’s not that unlikely an outcome for our basketball player to get 4 free throws out of 10. However, it would be pretty unlikely for him to get all 10.

### Instructions

The interactive visualization to the right demonstrates the concept of Binomial Distribution and how it relates to probability.

Try increasing the number of baskets that he attempts. What happens to the probability that he makes just one basket?

Now try increasing the number of baskets that we expect him to make. How does this affect the probability?

Now try changing how likely he is to make each basket. How does this affect the probability?

Continue to play around with the visualization. When you’re ready, continue to the next exercise.

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