Question

An important part of the customer service responsibilities of a cable company is the speed with which service troubles can be repaired. Historically, the data show that the likelihood is .75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that all five will be repaired on the same day

Answer 1

The probability is 0.2373

Explanation:

Here, we want to calculate the probability that the first 5 troubles reported on a given day were repaired on that same day.

Let P = probability that trouble reported same day is repaired = 0.75

q = probability that trouble reported is not repaired same day = 1-0.75 = 0.25

We now use the Bernoulli trial to approximate this probability of 5 being repaired same day

Mathematically, that would be;

5C5• p^5•q^0

= 5C5 * 0.75^5 * 0.25^0

= 1 * 0.2373046875 * 1

= 0.2373 approximately