Find the probability of throwing a sum of 4 at least 2 times

Find the probability of throwing a sum of 4 at least 2 times in 11 throws of a pair of fair dice.

Solution

There are 36 outcomes for throwing a pair of dice; 3 of these has a sum of ten (1,3), (2,2), and (3,1)

P(a sum of ten in 1 throw) = 3/36 = 1/12

This is a binomial distribution, either getting a sum of 4 or not in a throw, with p = 1/12, n = 4, x 4

P(x2) = P(x = 2) + P(x=3) + P(x=4)

P(x = 2)=

P(x = 3)=

P(x = 4)=