1. ## Probability/Expectation of game

Hey guys I'm having a hard time on this problem ... any help would be great!

In the game of "odd one out" three people each toss a fair coin to see if one of their coins shows a different face from the other two.
a) After one play, what is the probability of some person being the "odd one out"?
b Suppose play continues until there is an "odd one out". What is the probability that the duration is r plays?
c) What is the expected duration of play?

2. This is a geometric RV.

q=P(HHH or TTT)=1/4

So p=3/4 and E(X)=1/p=4/3

P(game takes r plays)= $pq^{r-1}$