Question

Capacitors are purchased from two independent sources A & B. The probability that the capacitors from A will not fail prior to x hours of use is e^(-.003x) and the probability that the capacitors from B will not fail prior to x hours is e^(-.005x). Given that the capacitors were observed to fail after between 50-60 hours of use. What is the probability that it was purchased from A?

Answer 1

here probability of purcahsing from A and B is not given therefore we are assuming it is 1/2 for both.

P(fail between 50-60 Hrs)=P(from A and fail between 50-60 Hrs+from B and  fail between 50-60 Hrs)

=(1/2)*(e^-0.003*60-e^-0.003*50)+(1/2)*(e^-0.005*60-e^-0.005*50​) =0.5*0.0254+0.5*0.0380

hence P(purchased from A given  observed to fail after between 50-60 hours of use)

=P(from A and fail between 50-60 Hrs)/P(fail between 50-60 Hrs) =0.5*0.0254/(0.5*0.0254+0.5*0.0380)

=0.4011