Question

A basketball player has made 80​% of his foul shots during the season. Assuming the shots are​ independent, find the probability that in​ tonight's game he does the following. ​a) Misses for the first time on his fourth attempt ​b) Makes his first basket on his fourth shot ​c) Makes his first basket on one of his first 3 shots

Answer 1

a)

Let the random variable X = number of trials until the first success occurs (such that number of successful attempt until first miss) and p is the probability of missing the foul shot (p = 1 - 0.80 = 0.20)

The random variable X follows geometric distribution with probability mass function,

Where, k is the number of trials.

Now, the probability of misses for the first time on his fourth attempt is,

b)

Let the random variable X = number of trials until the first success occurs (such that number of failed attempt until first success) and p is the probability of basket the foul shot (p = 0.80)

Now, the probability of makes his first basket on his fourth shot is,

c)

Let the random variable X = number of trials until the first success occurs (such that number of failed attempt until first success) and p is the probability of basket the foul shot (p = 0.80)

Now, the probability of makes his first basket on one of his first 3 shots