Answer:
25/216 or 0.1157
Explanation:
The probability of getting a 6 is 1/6.
The probability of not getting a 6 is 5/6
We roll a die 4 times and want 2 sixes, and 2 not sixes.
We want a combination of 2 sixes from 4 rolls, so we can use the binomial formula to solve this...
(4C2)(1/6)²(5/6)² = 6(1/36)(25/36) = (1/6)(25/36) = 25/216 = 0.1157
The long hand way of solving this is to list the 6 ways we can roll our desired result along with their probabilities...
We could get
6, 6, not 6, not 6 (1/6)(1/6)(5/6)(5/6) = 25/1296
6, not 6, 6, not 6 (1/6)(5/6)(1/6)(5/6) = 25/1296
6, not 6, not 6, 6 (1/6)(5/6)(5/6)(1/6) = 25/1296
not 6, not 6, 6, 6 (5/6)(5/6)(1/6)(1/6) = 25/1296
not 6, 6, not 6, 6 (5/6)(1/6)(5/6)(1/6) = 25/1296
not 6, 6, 6 not 6 (5/6)(1/6)(1/6)(5/6) = 25/1296
There are 6 different way this can happen, each having a probability of 25/196. We add up the probabilities, getting 150/1296, which reduces to
25/216