Question

10% of the bulbs produced in a factory are of red colour and 2% are red and defective. If one bulb is picked up at random, determine the probability of its being defective if it is red.

Answer 1

Let A and B be the events that the bulb is red and defective, respectively

P(A) = `10/100 = 1/10`.

P(A ∩ B) = `2/100 = 1/50`

P(B|A) = `("P"("A" ∩ "B"))/("P"("A"))`

= `1/50 xx 10/1`

= `1/5`

Thus the probability of the picked up bulb of its being defective, if it is red, is `1/5`.