Two cards are drawn successively without replacement from a well-shuffled deck of 52 cards. Find the probability of exactly one ace.

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Solution

$P (exactly one ace) = P (first card is ace) + P (second card is ace) = \frac{4}{52} \times \frac{48}{51} + \frac{48}{52} \times \frac{4}{51} = \frac{192 + 192}{52 \times 51} = \frac{384}{52 \times 51} = \frac{32}{221}$

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Two cards are drawn successively without replacement from a well-shuffled deck of 52 cards. Find the probability of exactly one ace.

Pexactly one ace=Pfirst card is ace +Psecond card is ace=452×4851+4852×451=192+19252×51=38452×51=32221

$P (exactly one ace) = P (first card is ace) + P (second card is ace) = \frac{4}{52} \times \frac{48}{51} + \frac{48}{52} \times \frac{4}{51} = \frac{192 + 192}{52 \times 51} = \frac{384}{52 \times 51} = \frac{32}{221}$