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Question
From a pack of well-shuffled cards, two cards are drawn at random. Find the probability that both the cards are diamonds when the first card drawn is replaced in the pack
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Solution
Let A ≡ the event that first card is diamond
B ≡ the event that second card is also a diamond
Since the first card is replaced in the pack, the two events A and B are independent.
∴ P(A ∩ B) = P(A)·P(B)
The probability of drawing one diamond card out of 52 cards is `13/52`.
∴ P(A) = P(B) = `13/52`
∴ P (both diamond cards) = P(A ∩ B)
= `13/52 xx 13/52`
= `1/16`.
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