Question

Dr. X has entered a dart‐throwing competition. Each time he throws a dart, he hits the bullseye with probability p, independent of any other throw. He throws the dart until he hits the bullseye, at which point his turn is over. Let N denote the number of times the dart is thrown. a. Find the pmf of PN(n) b. If p=0.15, what is the probability that Dr. X will throw the dart more than 4 times?

Answer 1

The random variable , which represents the number of times the dart is thrown until its hits the bulls eye for the first time is an example of the Geometric distribution, whose pmf is given by:

for all

where,

is the probability of success in each trial

In the given problem, .

The following probability is to be determined:

  

RESULT:

The probability that Dr. X will throw dart more than 4 times is 0.522