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A building contractor buys 70​% of his cement from supplier A and 30​% from supplier B....

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.

Solutions

Expert Solution

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

milcah answered 11 months ago
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