Thread: 3 Dice Are Rolled..Find Prob.

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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!!

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: .$\displaystyle 6^3 \:=\:216$ possible outcomes.

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

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

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

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