Question

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)

Answer 1

P ( A / sub ) = 0.5385

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