Question

Alice and Bob play a game that begins with flipping a fair coin twice. If the coin lands heads up on both flips, Bob wins. If the coin lands heads up on only one flip, Alice wins. If the coin lands tails up on both flips, they flip two more times, and this process continues until there is a winner. What is the probability that Bob wins the game?

Answer 1

0.25 (or
`(1)/(4)`)

Explanation:

As the coin is fair, there is an equal chance the coin lands on heads or tails, therefore:

Probability of heads = 0.5 (or
`(1)/(2)`)

Probability of tails = 0.5 (or
`(1)/(2)`)

For Bob to win, the coin must land on heads twice, To work this out, we multiply the two events together.

Probability of 2 heads = 0.5 (probability of landing heads up) x 0.5 (probability of landing heads up) = 0.25 (or
`(1)/(4)`)