I find this question challenging, hope to find an answer here,

Situation:

3 people play the game" odd men out". Each flips a coin simutaneously, if one face is different from the other two, its owner is the odd man, and he loses.

Question:

1) What is the probability that there is an odd men on an given turn, assuming all three coins are fair?

2) If there is no odd man on the 1st turn, all coins are flipped again, until an odd man is determined. What is the probability thateven number of turns are required to determined the odd man?

My Answer:

1)Let X be the number of odd man

X~Bin(3,0.5)

P(X=1) = (3C1)(0.5*2)(0.5)

= 0.375

2)this is where I get lost, should I be using geometric series here?