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  3. a building contractor buys 70?% of his cement from

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

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Basic Math

A building contractor buys 70?% of his cement from supplier Aand 30?% from supplier B. A total of 95?% of the bags from Aarrive? undamaged, and a total of 90?% of the bags from B arriveundamaged. Find the probability that a damaged bag is from supplierUpper A.

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4.2 Ratings (596 Votes)

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
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