Question

An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 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: Fewer than two troubles will be repaired on the same day?a. 6328b. 0010c. 0156d. 0146

Answer 1

c. 0.0156

Explanation:

The probability that fewer than two troubles will be repaired in the same day is the probability that exactly zero or exactly one trouble will be repaired on the same day. Let T be the number of troubles repaired:

`P(T=0) = (1-0.75)^5\\P(T=0)=0.0009766\\\\P(T=1) = 5(1-0.75)^4*0.75\\P(T=1)=0.014648\\\\P(T<2) = P(T=0)+P(T=1) = 0.014648+0.0009766\\P(T<2) =0.0156`

The probability that: Fewer than two troubles will be repaired on the same day is 0.0156.