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2 January, 00:23

You are dealt a hand of three cards, one at a time. Find the probability of each of the following. a) The first heart you get is the third card dealt. b) Your cards are all diamonds. c) You get no aces. d) You have at least one heart.

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  1. 2 January, 01:23
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    a) 0.145

    b) 0.013

    c) 0.783

    d) 0.586

    Step-by-step explanation:

    a) there are always 52 cards in total, 13 hearts

    Pa = 39/52 * 38/51 * 13/50 = 19266/132600 = 257/1700 = 0.145

    b) there are always 13 diamonds in a complete card

    Pb = 13/52 * 12/51 * 11/50 = 11/850 = 0.013

    c) there are always 4 aces, and 48 that are not aces

    Pc = 48/52 * 47/51 * 46/50 = 4324/5525 = 0.783

    d) there are 13 hearts, to get at least one heart we have.

    Pd = 1 - p

    Where p is the probability of no hearts

    p = 39/52 * 38/51 * 37/50 = 703/1700 = 0.414

    Pd = 1 - 0.414

    Pd = 0.586
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