Question

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 20​% fail in the first six months. Yours dies after you had it for three months. What are the chances that it has this​ flaw?
The probability that it has the flaw is ________?

Answer 1

Answer:

Step-by-step explanation:

Given that 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 20​% fail in the first six months.

Let A be the event that it fails in I 6 months

B1 = it has a flaw

B2 = it does not have a flaw

B1 and B2 are mutually exclusive and exhaustive

the chances that it has this​ flaw

=The probability that it has the flaw is

=$P(A/B_1)$=$\frac{P(B_1/A)P(A)}{P(B_1)} \\=\frac{0.80(P(A))}{0.50}$

To find P(A) = $P(AB1)+P(AB2)\\=0.5(0.8)+0.5(0.2)\\=0.5$

Hence required prob = 0.80