Question

Thirty percent of all telephones of a certain type are submitted for service while under warranty. Of these, 70% can be repaired, whereas the other 30% must be replaced with new units. If a company purchases ten of these telephones, what is the probability that exactly three will end up being replaced under warranty? (Round your answer to three decimal places.)

Answer 1

0.2669~0.267

Explanation:

Given that Thirty percent of all telephones of a certain type are submitted for service while under warranty.

Let x be the no of units being replaced out of 10 units purchased by a company under warranty

We have X has two outcomes either replaced or not. Also each unit is independent of the other

P(each unit fails and requires replaement ) = p =0.3

q =0.7

the probability that exactly three will end up being replaced under warranty

=P(X=3)

=
`10C3(0.3)^3(0.7)^7\\=0.2669`~0.267