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Math Help - Did I answer this correctly?

  1. #1
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    Did I answer this correctly?

    1. Popcorn sales in movie theaters break down as 40% plain popcorn and 60% buttered popcorn. While 65% of the plain popcorn is purchased by adults, 80% of the buttered popcorn is purchased by children. If a child purchases popcorn, what is the probability that it is buttered popcorn?

    MY ANSWER-------------------
    Plain Buttered Total
    Adults .26 .12 .38
    Children .14 .48 .62
    Total .40 .60 1



    When you figure up everything you get:
    Plain popcorn bought by adults-.40*.65=.26 or 26%
    Plain Popcorn bought by children-.40*(1-.65)=.40*.35=.14 or 14%
    Buttered Popcorn bought by the children-.60*.80=.48 or 48%
    Buttered Popcorn bought by adults-.60*(1-.80)=.60*.20=.12 or 12%

    Since 48% of all popcorn is buttered popcorn bought by children and 14% of all plain popcorn is bought by children then when you add those two together to get the total amount of popcorn bought by children you get 62%.

    Probability of a child buying popcorn is buying buttered popcorn=.48/.62=.77419 or 77.42%
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by jwells1999 View Post
    1. Popcorn sales in movie theaters break down as 40% plain popcorn and 60% buttered popcorn. While 65% of the plain popcorn is purchased by adults, 80% of the buttered popcorn is purchased by children. If a child purchases popcorn, what is the probability that it is buttered popcorn?
    Code:
    MY ANSWER-------------------
                     Plain         Buttered        Total
    Adults         .26           .12                .38
    Children       .14           .48                .62
    Total          .40           .60                  1

    When you figure up everything you get:
    Plain popcorn bought by adults-.40*.65=.26 or 26%
    Plain Popcorn bought by children-.40*(1-.65)=.40*.35=.14 or 14%
    Buttered Popcorn bought by the children-.60*.80=.48 or 48%
    Buttered Popcorn bought by adults-.60*(1-.80)=.60*.20=.12 or 12%

    Since 48% of all popcorn is buttered popcorn bought by children and 14% of all plain popcorn is bought by children then when you add those two together to get the total amount of popcorn bought by children you get 62%.

    Probability of a child buying popcorn is buying buttered popcorn=.48/.62=.77419 or 77.42%
    That looks OK

    RonL
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