In: Math
A building contractor buys 70% of his cement from supplier A and 30% from supplier B. A total of 95% of the bags from A arrive undamaged, and a total of 90% of the bags from B arrive undamaged. Find the probability that a damaged bag is from supplier Upper A.
P(supplier A) = 0.7
P(supplier B) = 0.3
P(undamaged | supplier A) = 0.95
P(undamaged | supplier B) = 0.9
P(undamaged) = P(undamaged | supplier A) * P(supplier A) + P(undamaged | supplier B) * P(supplier B)
= 0.95 * 0.7 + 0.9 * 0.3
= 0.935
P(damaged) = 1 - 0.935 = 0.065
P(damaged | supplier A) = 1 - P(undamaged | supplier A) = 1 - 0.95 = 0.05
P(supplier A | damaged) = P(damaged | supplier A) * P(supplier A) / P(damaged)
= 0.05 * 0.7 / 0.065
= 0.539