You are raising money for your club by calling old club members. You are asking for a $10 donation from each member. Each call is independent and has a probability of success of receiving $10 on any one call is 60%. You need to raise $100 and you stop when you’ve achieved that goal. What is the probability that you take exactly 15 calls to reach your goal.

The probability that you take exactly 15 calls to reach your goal is 0.1240.

Step-by-step explanation:

Let X = number of calls that result in receiving $10.

The probability that a call result in receiving $10 is, p = 0.60.

The number of calls made to reach a goal of $100 is, n = 15.

The random variable X follows a Binomial distribution with parameters n = 15 and p = 0.60.

The probability mass function of X is:

Now it is provided that it takes 15 calls to reach the goal, i.e. the 15th call was a success.

This implies that the probability of reaching the goal by the 15th call is same as the probability of 9 success in the previous 14 calls.

Compute the probability of 9 success in 14 calls as follows:

The probability of success in the 15th call is, 0.60.

Then the probability of reaching the goal by the 15th call

= P (X = 9) × 0.60

= 0.2066 × 0.60

=0.1240

Thus, the probability that you take exactly 15 calls to reach your goal is 0.1240.