Question

Find the expected number of events required to get three consecutive sixes on a dice, given that first two outcomes are two sixes

Answer 1

E_(n+1) = E_n + 1/6 * 1 + 5/6 *(1 +  E_(n+1))

E_(n+1)/6 = E_n + 1

E_(n+1) = 6 (E_n + 1)

So E_0 = 0, E_1 = 6, E_2 = 42, E_3 = 258...

Thanks