Geometric distribution - Wikipedia, the free encyclopediaA game is played by tossing two unbiased coins repeatedly until two heads are obtained in the same throw. The random variable X denotes the number of throws required. Find an expression for P(X=r)

Before playing the game, the player has to guess the value that X will take. If the player guesses correctly, he wins $5 . For an incorrect guess , the player loses $1. Suppose the player guesses X=t, express in terms of t, the expected amount won in a game.

I am not sure how to get the expression for part (1). If only one unbiased coin is tossed repeatedly, the probability of getting a head is

(0.5)+(0.5)^2+(0.5)^3+...

It's a infinite geometric series.

But how if two coins are tossed, does tree diagram work here?