A fait die is rolled untill a 1 appears or two consecutive 2

A fait die is rolled untill a 1 appears or two consecutive 2\'s appear.

a. Find the probability that the process ends with two consecutive 2\'s?

b. Find the expected number of rolls this process will take?

Solution

P(1) = 1/6

P(Consecutive 2\'s) = 1/36

a)

b) Total probability =1/6+1/36 = 0.194

Therefore, number of trials = 1/p = 5.14

Rounding off, number of trials = 6