. A company buys a large number of a particular part from 3 different suppliers

Question

. A company buys a large number of a particular part from 3 different suppliers A, B, and C. Seventy percent comes from A, 20 percent from B, and the rest from C. One percent of the parts from A are defective, 2 percent from B are defective, and 5 percent from C are defective. (a) What is the probability that one of these purchased parts selected at random is defective? (b) Given that a part is defective, what is the probability that it came from B? (c) Let D be the event that a randomly selected part is defective, and let A be the event that the part came from Suppler A. Are these two events independent? Explain

Explanation / Answer

P(supplier A) = 0.7

P(supplier B) = 0.2

P(supplier C) = 0.1

P(defective | supplier A) = 0.01

P(defective | supplier B) = 0.02

P(defective | supplier C) = 0.05

A) P(defective) = P(defective | supplier A) * P(supplier A) + P(defective | supplier B) * P(supplier B) + P(defective | supplier C) * P(supplier C)

= 0.01 * 0.7 + 0.02 * 0.2 + 0.05 * 0.1

= 0.016

B) P(supplier B | defective) = P(defective | supplier B) * P(supplier B) / P(defective)

= 0.02 * 0.2 / 0.016

= 0.25

C) P(D | A) = P(defective | supplier A) = 0.01

P(D) = P(defective) = 0.016

Since P(D | A) is not equal to P(D), these two events are not independent.

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