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by mstree on January 17th, 2008

mstree

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TerThere are 6 cookies in a jar. 3 chip, 2 butter and 1oatmeal. Eric picks a cookie from the jar w/out looking. Next,without replacing the 1st cookie, Eric picks a second cookie without looking. What is the probability that he will pick a chip & butter?

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Answers. 2 helpful answers below.

  • by Quirkie on January 18th, 2008

    Quirkie

    Let the six cookies be ABC chip DE butter and F oatmeal
    The ways of picking cookies: AB,AC,AD,AE,AF,BC,BD,BE,BF,CD,CE,CF,DE,DF,EF
    and the same combinations repeated the other way around.
    Thirty equally likely ways.
    In how many ways include the chip-butter combination:
    answer: AD,AE,BD,BE,CD,CE
    and the same thing the other way around = twelve combinations out of 30
    12/30 = 2/5

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  • by xprofessor on January 17th, 2008

    xprofessor

    Initially the probability of picking a chip cookie is 3/6 because 3 of the 6 cookies are chip. Then the chances of picking a butter cookie is 2/5 because 2 of the remaining 5 cookies are butter.

    The probability of both independent events occurring is the product of the individual probabilities: (3/6)(2/5) = 6/30 = 1/5.

    Note that by choosing a butter first and a chip second, the probability (2/6)(3/5) = 1/5 = the same as the first way.

    The probability that the first two draws will result in a chip cookie and butter cookie IN EITHER ORDER equals sum of the two individual ways of achieving it = 1/5 + 1/5 = 2/5.

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