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23 October, 11:12

Suppose that 6 cards are drawn what is the probability that all of them are black

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  1. 23 October, 12:53
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    The first card's probability is easy to calculate.

    Of the 52 cards, 26 are black, so the probability is

    (26 out of 52) or (1 out of 2) or. 5

    The second card will be drawn from 51 cards of which 25 are black:

    25 / 51

    Continuing with this pattern, drawing the 3rd card, the probability is

    24 / 50

    For the 4th card 23 / 49

    For the 5th card 22 / 48

    For the 6th card 21 / 47

    So, to get the probability of drawing all six cards AND getting all black, we multiply these 6 fractions:

    probability = (26 / 52) * (25 / 51) * (24 / 50) * (23 / 49) * (22 / 48) * (21 / 47)

    probability = 165,765,600 / 14,658,134,400

    probability = 0.0113087788306812
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