RubiM asked in Education & ReferenceTrivia · 1 decade ago

Two cards are drawn without replacement from an ordinary deck of 52. the chance neither of them is an ace?

on top of that, the probability that the first card is a king and the second is an ace?

1 Answer

  • J. J..
    Lv 7
    1 decade ago
    Favorite Answer

    There are 4 aces in a deck. Therefore there are 48 non aces.

    Therefore the chance that the first card drawn is not an ace = 48/52

    The chances that the second card drawn is 47/51. (As the first card was not replaced there is one less card in the pack making 51, and one less non ace making 47)

    Therefore as both draws must not have an ace to satisfy your criteria you need to multiply the individual probabilities. 48/52 x 47/51 = 2256 / 2652 = 0.8507 or 85% to the nearest percent.

    There are 4 kings. Therefore the chance that the king is drawn first = 4/52.

    There are still 4 aces in the pack, but there is one less card for the second draw (a king has been drawn already). Therefore the probability of the second card being an ace = 4/51

    The probability that both these events occur is therefore 4/52 x 4/51 = 16/2652 = 0.0060 or 0.6% (rounding to the nearest percent this would be 1%)

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