Question

A building contractor buys 80% of his cement from supplier A and 20​% from supplier B. A total of 75​% of the bags from A arrive​ undamaged, while 85​% of the bags from B arrive undamaged. Find the probability that a damaged bag is from supplier Upper A.

Answer 1

P(supplier A) = 0.8

P(supplier B) = 0.2

P(undamaged | supplier A) = 0.75

P(damage | supplier A) = 1 - P(undamaged | supplier A) = 1 - 0.75 = 0.25

P(undamaged | supplier B) = 0.85

P(damage | supplier B) = 1 - P(undamaged | supplier B) = 1 - 0.85 = 0.15

P(damage) = P(damage | supplier A) * P(supplier A) + P(damage | supplier B) * P(supplier B)

                   = 0.25 * 0.8 + 0.15 * 0.2

                   = 0.23

P(supplier A | damage) = P(damage | supplier A) * P(supplier A) / P(damage)

                                      = 0.25 * 0.8 / 0.23

                                      = 0.8696 (ans)