Twenty percent of all telephones of a certain type are sub m

Twenty percent of all telephones of a certain type are sub mitted 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

P(service while under warranty) = 20%

Of those 20%, 60% can be repaired and 40% must be replaced by new units.

N = 10 --> total of 10 telephones

Now, 20% of those will need service, so, 20% of 10 ---> 2 phones will need to be serviced....

P(replaced under warranty) = 20% * 40% = 0.2 * 0.4 = 0.08
P(repaired under wanrranty) = 60% * 20% = 0.12
P(no need of service) = 100% - 20% = 80% = 0.8

IF 2 are replaced under warranty, then the other 8 will have to need no service or must be repaired under warranty, which has a probability of 0.8 + 0.12 = 0.92

P(2 replaced under warranty) = 10C2 * (0.08)^2 * (0.92)^8

45 * (0.08)^2 * (0.92)^8

0.1478070354636177 ---> ANSWER