Question

If you are rolling 3 dice, what is the probability of rolling 2 sixes?

Answer 1

Probability of rolling two sixes in 3 dice is `15/216`

Explanation:

This is an example of binonmial distribution of general form `X~B(n,p)` Here `n=3` i.e no of dice thrown. and `p=1/6`i.e probability of rolling `6` in single dice.
`P(n,r(2)) = nc_r p^r*q^(n-r)` where `r=2` (rolling of two sixes) and `q=5/6` i.e probability of not rolling `6` in single dice.

So probability of rolling two sixes in 3 dice is `P(n,r(2)) = nc_r p^r*q^(n-r) or 3c_2*(1/6)^2.(5/6)^(3-2) =3*1/36*5/6=15/216`[Ans]