Twenty percent of all telephones of a certain type are submi

Twenty percent of all telephones of a certain type are submitted for service while under warranty. Of these. 60% can be repaired, whereas the other 40% must be replaced with new units. If a company purchases ten of these telephones, what is the probability that exactly two will end up being replaced under warranty?

Solution

Let T represent a telephone, given to the service while under warranty and should be replaced.

Let r = replaced, s = submitted

Then p = P(T) = P(r|s).P(s) = 0.4*0.2 = 0.08

and X is the number of telephones that must be replaced among the 10 telephones of the company.

Now binomial distribution with n= 10, p = 0.08

Hence we can say p(X = 2) = p(2) = ¹⁰C₂*(0.08)²(0.92)⁸ = 0.1478