what is the expected number of rolls of a loaded sixsided di

what is the expected number of rolls of a loaded six-sided die to get 5 two\'s. The porbability distibution is as follow: the probability of rolling a 1, 3, or 5 is 1/6. The probability of rolling a 4 or 6 is 1/4. And the probability of rolling a 2 is 1/3.

Solution

Here the probability of getting 2 is 1/3.

So P(2,2,2,2,2) = 1/2*1/2*1/2*1/2*1/2= 1/32.