# A Game of Coin and Die

This game is played with a fair coin and a die. First player flips a coin. If it turns out head(H), the player proceeds with tossing a die. If it turns out tail(T), the player proceeds with flipping a coin for the second time. The player wins if it gets head on the first tossing and 6 on the second or tails on both flips of coin. What is the probability of winning a game?

• Your rules of winning are a bit confusing. Should it be: "The player wins if (1) the first coin toss is H and the subsequent die roll is 6 or (2) both coin flip are tails."? – jdods May 3 '16 at 22:52

P(head on the first flip and 6 on the second tossing)=P(head on the first flip)*P(6 on the second tossing)=$\frac{1}{2}*\frac{1}{6}=\frac{1}{12}$
P(tails on both flip)=$\frac{1}{2}*\frac{1}{2}=\frac{1}{4}$
P(winning the game)=P(head on the first flip and 6 on the second tossing)+P(tails on both flip)=$\frac{1}{12}+\frac{1}{4}=\frac{1}{3}$