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Math Help - 3 Dice Are Rolled..Find Prob.

  1. #1
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    Exclamation 3 Dice Are Rolled..Find Prob.

    Please Help--

    Three fair dice are rolled (1Red 1Green 1Blue); Find the probability that the largest number obtained is 5 (there has to be at least one 5 in every roll but cannot have 6s).

    Thank you!!
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  2. #2
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    Hello, bjanela!

    Three fair dice are rolled (1 Red, 1 Green, 1 Blue).
    Find the probability that the largest number obtained is 5.
    (There must be at least one 5 in every roll, but cannot have 6s).
    There are: . 6^3 \:=\:216 possible outcomes.

    How many has no 6s?
    . . There are: . 5^3 \:=\:125 outcomes with no 6s.

    Among these outcomes, how many have no 5s?
    . . There are: . 4^3 \:=\:64 outcomes with no 5s and no 6s.

    Hence, there are: . 125-64 \:=\:61 outcomes with some 5s and no 6s.

    Therefore: . P(\text{some 5s and no 6s}) \;=\;\frac{61}{216}

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