An inspector working for a manufacturing company has a 99% chance of correctly identifying defective items and a 0.5% chance of incorrectly classifying a good item as defective. The company has evidence that its line produces 1.0% of defective items. Round your answers to five decimal places (e. g. 98.76543). (a) What is the probability that an item selected for inspection is classified as defective?

The probability that an item selected for inspection is classified as defective is 0.01485.

Step-by-step explanation:

Denote the events as follows:

A₁ = an item produced by the company is defective.

A₂ = an item produced by the company is not defective.

X = an item is classified as defective by the inspector.

Given:

P (X|A₁) = 0.99

P (X|A₂) = 0.005

P (A₁) = 0.01

P (A₂) = 1 - P (A₁) = 1 - 0.01 = 0.99

The law of total probability states that:

Use this law to compute the probability that an item selected for inspection is classified as defective as follows:

Thus, the probability that an item selected for inspection is classified as defective is 0.01485.

the answer is 13/48

step-by-step explanation: