Question

An inspector working for a manufacturing company hasa 99% chance of correctly identifying defective items and a 0.5% chance of incorrectly classifyinga good item as defective. The company has evidence that 0.9% of the items its line produce isnonconforming.(a) What is the probability that an item selected for inspection is classified as defective

Answer 1

Explanation:

From the given information:

Let A be the event where an item is identified as defective;

B₁ to be the event where an item is actually defective

B₂ to be the event that the item is good

So;

P(B₁) = 0.009

P(B₂) = 0.991

Probability that an item is classified as defective when it is actually defective is P(A|B₁) = 0.99

Probability that an item is classified as defective when it is actually good is P(A|B₂) = 0.005

∴

Probability of classifying a product as defective = P(A)

P(A) = P(A|B₁) × P(B₁) + P(A|B₂) × P(B₂)

P(A) = 0.99 × 0.009 + 0.005 × 0.991

P(A) = 0.0139

P(A) = 1.39%