You keep tossing a fair coin until you get two consecutive t

You keep tossing a fair coin until you get two consecutive \"tails\". Find the probability distribution of Y, the number of tosses needed.

This question is simple enough, but I\'m confused what the \'probability distribution\' in this context is, since there\'s a countably infinite number of possible coin flips needed. I know the expected value is 6, but the distribution I\'m not so sure about..

Thanks for any help :)

Solution

x-----------P(x)

0 ---------1/3

1----------1/3

2----------1/3