Question

(b) At a factory where bolts are produced, machines A, B, C produce respectively 25%, 35% and 40% of all bolts. Of the output of these machines, defects constitute 5%, 4% and 2% respectively. A bolt selected at random from the production turned out to be defective. What machine was the most likely to have produced this defective bolt? (give the probability it was this machine.) [5]

Answer 1

(b) P(Machine A) = 0.25

P(Machine B) = 0.35

P(Machine C) = 0.40

P(Machine A produce defective bolt) = 0.05

P(Machine B produce defective bolt) = 0.04

P(Machine C produce defective bolt) = 0.02

A selected bolt at random from the producton and that was defective.

First we will find probability of finding one defective bolt by total probability theorem

P(Defective) = 0.25 * 0.05 + 0.35 * 0.04 + 0.40 * 0.02 = 0.0345 or 3.45%

Here,

P(The bolt is from machine A) = 0.25 * 0.05/0.0345 = 36.23%

P(The bolt is from machine B) = 0.35 * 0.04/0.0345 = 40.58%

P(The bolt is from machine C) = 0.40 * 0.02/0.0345 = 23.19%