Question
Two friends worked together on an entry for a poetry contest and won; however, there is only one prize and it cannot be split. Some methods of determining who receives the prize are given below.
Select all the fair methods for determining who receives the prize.
roll a die and evaluate the outcome as either even or odd
throw a stone closest to an object
ask a random friend to choose
place both names in equal amounts into a hat and draw one without looking
ask a stranger to flip a coin
Select all the fair methods for determining who receives the prize.
roll a die and evaluate the outcome as either even or odd
throw a stone closest to an object
ask a random friend to choose
place both names in equal amounts into a hat and draw one without looking
ask a stranger to flip a coin
Answers
GPT-4o mini
Here are the methods that can be considered fair for determining who receives the prize:
1. **Roll a die and evaluate the outcome as either even or odd** - If both friends agree beforehand on which outcome (even or odd) corresponds to which person, and the die is rolled fairly, this is a fair method.
2. **Throw a stone closest to an object** - This method can be fair if both friends have an equal chance to be successful in throwing the stone and if the object is neutral (not favoring either person).
3. **Ask a random friend to choose** - If the friend is unbiased and does not have a preference for either person, this can be considered a fair method.
4. **Place both names in equal amounts into a hat and draw one without looking** - This is a classic fair method since both friends have an equal probability of being selected.
5. **Ask a stranger to flip a coin** - This method is fair if each friend agrees on which side of the coin corresponds to whom. A fair coin flip gives an equal probability of winning for both friends.
Therefore, all the listed methods (1 to 5) can be considered fair, provided they are executed without bias and both friends agree on the procedures beforehand.
1. **Roll a die and evaluate the outcome as either even or odd** - If both friends agree beforehand on which outcome (even or odd) corresponds to which person, and the die is rolled fairly, this is a fair method.
2. **Throw a stone closest to an object** - This method can be fair if both friends have an equal chance to be successful in throwing the stone and if the object is neutral (not favoring either person).
3. **Ask a random friend to choose** - If the friend is unbiased and does not have a preference for either person, this can be considered a fair method.
4. **Place both names in equal amounts into a hat and draw one without looking** - This is a classic fair method since both friends have an equal probability of being selected.
5. **Ask a stranger to flip a coin** - This method is fair if each friend agrees on which side of the coin corresponds to whom. A fair coin flip gives an equal probability of winning for both friends.
Therefore, all the listed methods (1 to 5) can be considered fair, provided they are executed without bias and both friends agree on the procedures beforehand.