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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.
Solution
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`.
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