Question

A basketball player shoots free throws. the number of free throws made is recorded. Define a random variable so that it is Bernoulli.

Answer 1

Here basketball player shoots free throws:

So each free throw is independent of other. And outcome is dichotomous (either score a goal or miss). This satisfies the condition of Bernoulli distribution

Here Let X be the random variable being number of scores out of n-free attempts by the basketball player

Let p be the success probability of scoring a goal

So q=1-p is the probability of missing the goal

So now probability of the basketball player having k scores out of n free throws is given below:

P (X=k scores) is given by nCk (p)k(q)n-k