Suppose that John hands you a coin to flip and wants to bet on the outcome. Now, John has tried this sort of thing before, and you suspect that the coin is "rigged." You decide to test this hypothesis by taking a sample. You flip the coin twice, and it is heads both times. You say, "Aha, I knew it was rigged!" John replies, "Don't be silly. Any coin can come up heads twice in a row."
The following scheme was devised to allow fair results even if the coin is somewhat biased. The coin is flipped twice. If it comes up heads both times or tails both times, it is flipped twice again. If it comes up heads-tails, this will decide the outcome in favor of the first party; and if it comes up tails-heads, this will decide the outcome in favor of the second party. Will this result in a fair toss even if the coins are biased?

A) No
B) Yes

Question

Suppose that John hands you a coin to flip and wants to bet on the outcome. Now, John has tried this sort of thing before, and you suspect that the coin is "rigged." You decide to test this hypothesis by taking a sample. You flip the coin twice, and it is heads both times. You say, "Aha, I knew it was rigged!" John replies, "Don't be silly. Any coin can come up heads twice in a row." ​
The following scheme was devised to allow fair results even if the coin is somewhat biased. The coin is flipped twice. If it comes up heads both times or tails both times, it is flipped twice again. If it comes up heads-tails, this will decide the outcome in favor of the first party; and if it comes up tails-heads, this will decide the outcome in favor of the second party. Will this result in a fair toss even if the coins are biased?
​
A) No
B) Yes

Quizplus · Accepted Answer

This scheme will result in a fair toss even if the coins are biased. This is because if the coin is biased towards heads, for example, the probability of getting heads-heads or tails-tails in the first two tosses is higher, but if that happens, the coin is flipped again until either heads-tails or tails-heads appear, which has an equal probability of 1/2. Therefore, the overall probability of either party winning is 1/2, which is a fair toss.

Suppose That John Hands You a Coin to Flip and Wants