A bag has 4 chocolate, 7 lollipops, and 5 gumballs. If you select 5 randomly, what is the probability that you select all the same type?

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  • Favorite Answer

    You start with 16 candies

    All lollipops:

    (7/16) * (6/15) * (5/14) * (4/13) * (3/12) =>

    (7/16) * (2/5) * (5/14) * (4/13) * (1/4) =>

    (7/14) * (2/16) * (5/5) * (4/4) * (1/13) =>

    (1/2) * (1/8) * 1 * 1 * (1/13) =>

    1/208

    All gumballs:

    (5/16) * (4/15) * (3/14) * (2/13) * (1/12) =>

    (5 * 12 * 2) / (16 * 15 * 14 * 13 * 12) =>

    (5 * 2) / (16 * 15 * 14 * 13) =>

    1 / (8 * 3 * 14 * 13) =>

    1 / (104 * 3 * 2 * 7) =>

    1 / (208 * 21)

    We can't pull 5 chocolates.  Add the probabilities together.

    1/208 + 1/(208 * 21) =>

    21 / (21 * 208) + 1 / (208 * 21) =>

    (21 + 1) / (21 * 208) =>

    22 / (21 * 208) =>

    11 / (21 * 104) =>

    11 / 2184

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  • 1 month ago

    I've got it. We can do 7C5+5C5 (lollipops and gumballs respectively while ignoring chocolate bars as that can't be done). Over the total which is 16C5.

    22/4368

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  • 1 month ago

    Total objects = 4 + 7 + 5 = 16

    Ratios:

    Chocolate --> 4/16 = 25% (0.25) ---> 1.25 if selected randomly 5 times

    Lollipops --> 7/16 = 44% (0.4375)---> 2.20 if selected randomly 5 times

    Gumballs --> 5/16 = 31% (0.3125)---> 1.56 if selected randomly 5 times

    -Cannot recall for second part of the question, sorry. 

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