Say you roll two dice what is the probability that the sum o

Say you roll two dice what is the probability that the sum of the dice is 6 twice consecutively before the first total of 2 ? I am trying to condition on the first roll so either 7 occurs 12 occurs or neither and then if neither then start again.

Solution

P( getting 2 consecutive 6 before getting a total of 2)

i.e. P( Sum of first two dice is six and the third die is Sum of 2)

= P( getting a sum of six on the first throw) × P( getting a sum of six on the second throw) × P( getting a sum of 2 on the third throw)

= (2/36) × ( 2/36) × (1/36)

= 0.000086