Question

A factory production line is manufacturing bolts using three machines, A, B and C. Of the total output, machine A is responsible for 25%, machine B for 35% and machine C for the rest. It is known from previous experience with the machines that 5% of the output from machine A, 4% from machine B and 2% from machine C is defective. A bolt is chosen at random from the production line and found to be non - defective. What is the probability that it came from machine A? Round answer to 4 decimal places.

Answer 1

Contingency table as per information:

Machines	% Output	Defective	Non defective
A	25%	5%	95.00%
B	35%	4%	96.00%
C	40%	2%	98.00%

P(Machine A / Non defective) = P(Machine A and Non defective) / P(Non defective)

P(Machine A / Non defective) = (0.25 * 0.95) / (0.25 * 0.95) + (0.35 * 0.96)+ (0.40 * 0.98)

P(Machine A / Non defective) = 0.2375 / 0.9655

P(Machine A / Non defective) = 0.2460

ANS: Probability that a non defective bolt is from machine A = 0.2460