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Question
Two cards are drawn one after the other from a pack of 52 cards without replacement. What is the probability that both the cards drawn are face cards?
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Solution
Let A ≡ the event that first card is a face card
B ≡ the event that second card is a face card
Since there are 12 face cards in the pack of 52 cards,
P(A) = `12/52 = 3/13`
`"P"("B"//"A")` = Probability that second card is a face card under the condition that first face card is not replaced. When the second card is drawn, the pack has 51 cards including 11 face cards.
∴ `"P"("B"//"A") = 11/51`
∴ the required probability = P(A ∩ B)
= `"P"("A")*"P"("B"//"A")`
= `3/13 xx 11/51`
= `11/221`.
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