If a fair, #6#-sided die is rolled #5# times, what is the probability that there are exactly #3# sixes?

1 Answer
MathFact-orials.blogspot.com
Jun 7, 2018

#((5),(3))xx(1/6)^3xx(5/6)^2~~0.0322#

Explanation:

There is a probability of #1/6# of rolling a 6 on a 6-sided die.

The probability of rolling three 6s, therefore, is #(1/6)^3#.

The probability of not rolling a 6 is #(5/6)# and the probability of not rolling a 6 twice is #(5/6)^2#

There are #((5),(3))=10# different ways to roll three 6s in 5 tries.

All together then, we have:

#10xx(1/6)^3xx(5/6)^2~~0.0322#

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