Question

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

Answer 1

`((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`