# Coin flipping

#### v-moda

##### New Member
Alan, Bob, and Charlie agreed that the “odd man” (the person whose outcome is
different from others) would buy the coffee. After simultaneously flipping their
coins, Bob turned up with the only “tail”. At this point Bob demanded to Alan’s
and Charlie’s coins. He discovered that Alan had used a two-headed coin. With
this Bob accused Alan of cheating and refused to buy. Charlie, however, insisted
that even with Alan’s suspicious coin the game was fair and therefore Bob was
obliged to buy. Under the circumstances, what was each man’s probability of
losing? Do you agree with Charlie?

This was the question. I was thinking since Charlie has two headed coins, the total combination for all players should be 2x2 =4. The results would be:
HHH, HTT, HTH, HHT
According to this result, all players have an equal chance of winning. (Probability of 1/4). This is was I thought. Not quite sure if this is the correct logic. A guide is needed. Thanks.
The text passage describes a scenario involving a coin flipping game and a dispute over the fairness of the game. It also includes an analysis of the probabilities by one of the participants.
single_question_with_answer

the passage contains a single mathematical question about the probability of each man losing in the coin flipping game, and an attempt at answering this question is provided by the participant.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Coin flipping

#### v-moda

##### New Member
Alan, Bob, and Charlie agreed that the “odd man” (the person whose outcome is
different from others) would buy the coffee. After simultaneously flipping their
coins, Bob turned up with the only “tail”. At this point Bob demanded to Alan’s
and Charlie’s coins. He discovered that Alan had used a two-headed coin. With
this Bob accused Alan of cheating and refused to buy. Charlie, however, insisted
that even with Alan’s suspicious coin the game was fair and therefore Bob was
obliged to buy. Under the circumstances, what was each man’s probability of
losing? Do you agree with Charlie?

This was the question. I was thinking since Charlie has two headed coins, the total combination for all players should be 2x2 =4. The results would be:
HHH, HTT, HTH, HHT
According to this result, all players have an equal chance of winning. (Probability of 1/4). This is was I thought. Not quite sure if this is the correct logic. A guide is needed. Thanks.
user
The text passage describes a scenario involving a coin flipping game and a dispute over the fairness of the game. It also includes an analysis of the probabilities by one of the participants.

TYPE: SINGLE_QUESTION_WITH_ANSWER

The passage contains a single mathematical question about the probability of each man losing in the coin flipping game, and an attempt at answering this question is provided by the participant.