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dvd_clapp
dvd_clapp asked in Science & MathematicsMathematics · 1 decade ago

Statistics question on probability?

You are dealt a hand of 3 cars one at a time (without replacement) from a standard deck of 52 cards. Find the probability that at least one of the cards is a heart.

Thanks.

2 Answers

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  • A conscience
    Lv 6
    1 decade ago
    Favorite Answer

    one heart:

    3 choose 1 to be heart=3

    13/52 chance of that one being heart.

    3(13/52)=39/52

    Two hearts:

    3 choose 2 to be heart=3

    (13/52)(12/51)=3/51chance of two hearts.

    3(3/51)=9/51

    three hearts:

    3 choose 3 to be heart=1

    (13/52)(12/51)(11/50)=33/2550 chance of three hearts.

    1(33/2550)=33/2550

    add them all together: 39/52+9/51+33/2550=4791/5100 chance of at least 1 heart.

  • kelby7670
    Lv 7
    1 decade ago

    probability of no hearts = 39/52 * 38/51 * 37/50 = 0.4135

    so probability of at least one is 1-0.4235 =0.5864

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