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!!
Hello, bjanela!
There are: .$\displaystyle 6^3 \:=\:216$ possible outcomes.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).
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: .$\displaystyle P(\text{some 5s and no 6s}) \;=\;\frac{61}{216}$