Question

Drink dispensers fail with a probability of 0.01. When the dispenser fails, the business suffers losses that month with a 0.8 probability, but sometimes the business suffers monthly losses without the dispensers failing, this happens 10% of the time. If there have been losses this month, calculate the probability that the dispensers haven't failed.

Answer 1

Let's assume

Probability for losses this month = P(B)

Probability for dispensers have not failed = P(A)

P(B) = Probability of dispenser failed * Prob of monthly losses + Probability of not failed * Prob of monthly losses

=(0.01*0.8) +(0.99*0.1) = 0.179

P(A) = 0.99

P(B|A) = Probability of losses given dispensers have not failed = 0.1

Now , from baye's theorem P(A|B) = Probability of dispensers have not failed given losses = P(B|A) * P(A) / P(B)

= (0.1 * 0.99) / 0.179

= 0.553

Please revert back for any doubt.