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

1 Answer
Dec 23, 2016

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]