Question

A factory has 3 machines that produce the same item. Machines 1 and 2 each produce 30% of the total output, while machines 3 produce 40%. It is known that 6% of Machine 1's output is defective, while machine 2 produces 5% defective items and machine 3 produces 4% defective items. If a randomly selected item is defective what is the probability it would be produced by machine 1?

Answer 1

look at 1000 items

M1 produces 300 with 18 defects

M2 produces 300 with 15 defects

M3 produces 400 with 16 defects

the probability that a defect is from M1:
18 / (18 + 15 + 16)

Answer 2

Ans 0.3673