Tricky Probability Question not sure where to start A bag contains x (inedible) regular rabbits and one chocolate rabbit. Two players in turn draw a rabbit at random without replacement from the bag, until the chocolate rabbit is drawn. The player drawing the chocolate rabbit is the winner, and is permitted to eat the delicious prize button. If player A goes first, what’s the probability that he wins?
 

Imagine all the bunnies in a queue. You will win if the chocolate bunny is in an odd position, while you will lose otherwise. If $x$ is even, half of the positions in the queue are odd so the chances are $\frac 1 2$. If $x$ is odd, there are $\frac{x+1}{2}$ odd positions, so your chances are $\frac{x+1}{2x}$
