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Question
Two cards are drawn from a pack of 52 cards. Find the probability that one is club and the other is a diamond.
Solution
Two cards can be drawn from a pack of 52 cards in 52C2 = `(52 xx 51)/(1 xx 2)` = 26 × 51 ways
∴ n(S) = 26 × 51
Let B = the event that one is club and the other is a diamond.
One club can be drawn from 13 clubs in 13C1 = 13 ways
Similarly, one diamond can be drawn in 13 ways
∴ one club and one diamond can be drawn in 13 × 13 ways
∴ n(B) = 13 × 13
∴ the reqwred probability= P(B) = `("n"("B"))/("n"("S"))`
= `(13 xx 13)/(26 xx 51)`
= `13/102`
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