# What calculation was used to determine the probability of this exercise?

### Question

In the context of this exercise, what calculation was used to determine the probability of making an exact number of baskets?

The calculation used is known as the Probability Mass Function. This gives us the probability of getting exactly “r” successes in “n” trials.

The calculation is as follows,
`Probablity of r = nCr * (p^r) * (1-p)^(n-r)`

p = Probability of making a basket.
n = number of trials.
r = number of specific events to obtain.

This gives us the `Probability of making exactly "r" out of "n" baskets`.

`nCr` is the combination, or “n choose r” operation. The formula for this is
`n! / (r! * (n - r)!)`

As an example,

``````'''
Given the probability of making a basket as: 0.5.
What is the probability of making exactly 2 out of 5 baskets?

Plugging this into our equation, we have
(5 C 2) * (0.5^2) * (1-0.5)^(5-2)
= 10 * 0.25 * 0.125
= 0.31
'''
``````

Feel free to try out different values in the exercise, and see how this works!

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What is “C” in the formula?

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Combination (From the ‘Permutation and Combination’ topic in Mathematics)

`nCr` is the combination, or “n choose r” operation. The formula for this is
`n! / (r! * (n - r)!)`

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