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23 April, 04:38

Suppose that 5 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 5 are not black?

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  1. 23 April, 06:17
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    Here's the way I see it: 5 cards are drawn, one by one, without replacement. Half (or 26) of the original deck are black and half (26) are white.

    P (5 are not black) = P (5 are red)

    P (5 are not black) = P (first card is red) * P (second card is red) * P (third card is red) * P (fourth card is red) * P (fifth card is red) =

    (26/52) * (25/51) * (24/50) * (23/49) * (22/48) = 0.025 (answer)

    We start with 52 cards. We draw one, leaving 51 cards, 25 of which are red. And so on.
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