In a bulb factory, machines A, B and C manufactures 60%, 30% and 10% bulbs respectively. Out of these bulbs 1%, 2% and 3% of the bulbs produced respectively by A, B and C are found to be defective. A bulb is picked up at random from the total production and found to be defective. Find the probability that this bulb was produced by machine A.

Question

Philoid · Accepted Answer

Let A : Manufactured from machine A

B : Manufactured from machine B

C : Manufactured from machine C

D : Defective bulb

We want to find P(A|D), i.e. probability of selected defective bulb is from

machine A

Conclusion: Therefore, the probability of selected defective bulb is from machine A is