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Question
Three cards are drawn from a pack of 52 cards. Find the chance that at least one is a diamond card
Solution
3 cards can be drawn from a pack of 52 cards in 52C3 ways.
∴ n(S) = 52C3
Let event B: Out of the three cards drawn, at least one is a diamond.
∴ B' is the event that all 3 cards drawn are non-diamond cards.
In a pack of 52 cards, there are 39 non-diamond cards.
∴ 3 non-diamond cards can be drawn in 39C3 ways
∴ n(B') = 39C3
∴ P(B') = `("n"("B'"))/("n"("S"))`
= `(""^39"C"_3)/(""^52"C"_3)`
= `(39 xx 38 xx 37)/(52 xx 51 xx 50)`
= `703/1700`
∴ P(B) = 1 – P(B')
= `1 - 703/1700`
= `997/1700`
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