Question

A factory has two Machines-I and II. Machine-I produces 60% of items and Machine-II produces 40% of the items of the total output. Further 2% of the items produced by Machine-I are defective whereas 4% produced by Machine-II are defective. If an item is drawn at random what is the probability that it is defective?

Answer 1

Let A₁ be the event that items are produced by machine – I, A₂ be the event that items are produced by machine – II.

Let B be the event of drawing a defective item.

We have to find the total probability of event B.

That is P(B) clearly A₁ and A₂ are mutually exclusive and exhaustive events.

∴ P(B) = P(A₁) . P(B/A₁) + P(A₂) . P(B/A₂)

Given P(A₁) = `60/100` = 0.60

P(B/A₁) = `2/100` = 0.02

P(A₂) = `40/100` = 0.40

P(B/A₂) = `4/100` = 0.04

P(B) = P(A₁) . P(B/A₁) + P(A₂) . P(B/A₂)

= 0.60 × 0.02 + 0.40 × 0.04

= 0.012 + 0.016

= 0.028