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23 November, 07:02

There are two kinds of products in a warehouse, A and B. The percentage of A is 70%, B is 30%. The probability of substandard products in A is P (A = sub) = 2.5%, for B, it's P (B = sub) = 5%. Warehouse tests 4 products and one of them is substandard. What is the probability that this product is from A, P (this sub from A)

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  1. 23 November, 09:57
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    P (A / sub) = 0.5385

    Step-by-step explanation:

    Given:

    P (A) = 0.7

    P (B) = 0.3

    P (sub / A) = 0.025

    P (sub / B) = 0.05

    Asked: P (A / sub)

    This is the case of conditional probability where we chosen a substandard product which could come fro either A or B, we need to determine the probability of it belonging to A.

    P (A / sub) = P (A and sub) / P (sub)

    P (A and sub) = 0.7 * 0.025 = 0.0175

    P (sub) = 0.7*0.025 + 0.3*0.05 = 0.0325

    P (A / sub) = 0.0175 / 0.0325

    P (A / sub) = 0.5385
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