Daniel and Ann alternatively toss a fair coin. Daniel tosses the coin first, then Ann tosses the coin, then it is again Daniel's turn and so on. We record the sequence. If there is a head followed by a tail the game ends and the person who tosses the tail wins. What is the probability that Daniel wins the game?

Hint: Call the event of Daniel winning the game A, and let x = P(A). Also, let B denote the event that Daniel sees a Head in the first toss. Use the law of total probability to write down:

P(A) = P(A|B)P(B) + P(A|B c )P(B c ).