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)

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