Roll two standard dice and add the numbers. What is the probability of getting a number larger than 4 for the first time on the third roll?

Answer 1

There are 4 ways to roll at most 4: 11, 12, 21, 22
rolling more than 4 on 3rd roll is thus
P(2-4) * P(2-4) * (1-P(2-4)) = 4/36 * 4/36 * 32/36 = 8/729