# Check your intuition

**Discrete Mathematics**Level 3

Suppose Charlotte and Beatrice play a coin-flipping game with biased coins. The game iterates as per this rule:

Start at step 1. At step n, flip a coin with \(\frac{1}{2^n+2}\) probability of coming up heads and \(\frac{2^n+1}{2^n+2}\) probability coming up of tails. If heads comes out, Beatrice wins. Else, proceed to step n+1.

What is the probability that Beatrice wins?