Some electronic devices are better used than new The failure

Some electronic devices are better used than new. The failure rate is higher when they are new than when they are six months old. For example, half of the personal music players sold by a particular brand have a flaw. If the player has the flaw, it dies in the first six months. If it does not have this flaw, then only 15% fail in the first six months. Yours dies after you had it for three months. What are the chances that it has this flaw?

Solution

This is a conditional probability -

Let, A be the event that the player has flaw.

B be the event that dies within six months.

so use Pr(A given B)=Pr(A and B) / Pr(B).

Pr(has flaw given dies within 6 months)=
Pr(has flaw and dies within 6 months) / Pr(dies within 6 months) = .75 / (.75(1) + .25(.30))=
.25/.3625= 0.909

The probability that it has the flaw is 0.909