MATH SOLVE

4 months ago

Q:
# 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 ________?

Accepted Solution

A:

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 monthsB1 = it has a flawB2 = it does not have a flawB1 and B2 are mutually exclusive and exhaustive the chances that it has this flaw=The probability that it has the flaw is=[tex]P(A/B_1)[/tex]=[tex]\frac{P(B_1/A)P(A)}{P(B_1)} \\=\frac{0.80(P(A))}{0.50}[/tex]To find P(A) = [tex]P(AB1)+P(AB2)\\=0.5(0.8)+0.5(0.2)\\=0.5[/tex]Hence required prob = 0.80