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Sagot :
To determine which situations are both statistically fair and morally fair, we need to evaluate each situation individually based on these criteria:
### Situation 1:
Description: A high school student decides whether to clean his room or do his homework by picking a tile at random from a bag of lettered tiles. If he picks a consonant, he will clean his room, and if he picks a vowel, he will do his homework.
Evaluation:
- Statistically fair: There are 21 consonants and 5 vowels in the English alphabet. The probability of picking a consonant is much higher (21/26) than picking a vowel (5/26). Therefore, it is not statistically fair.
- Morally fair: There are no moral issues involved.
Conclusion: Not statistically fair.
### Situation 2:
Description: Four candidates eligible for a vacancy at a company are evaluated by writing their names on pieces of paper, shuffling the papers, and drawing one at random.
Evaluation:
- Statistically fair: Each of the four candidates has an equal 1/4 chance of being selected.
- Morally fair: Ignoring qualifications and experience for a job can be considered inappropriate. It does not account for merit.
Conclusion: Not morally fair.
### Situation 3:
Description: Five cousins decide which board game to play by writing their preferred game on different sections of a spinner. The spinner has five equally-sized sections, and they will play the game written on the section where the spinner lands.
Evaluation:
- Statistically fair: Each game has exactly 1/5 chance of being selected, which is fair.
- Morally fair: All five cousins have an equal opportunity for their game to be played, so it is morally fair.
Conclusion: Both statistically and morally fair.
### Situation 4:
Description: Kate picks a tile at random from a collection of five tiles numbered 2 through 6. Kate chooses the picnic spot if she picks a prime number (2, 3, 5), and Charles chooses if Kate picks a composite number (4, 6).
Evaluation:
- Statistically fair: There are 3 prime numbers and 2 composite numbers out of the five tiles, so it is not statistically fair.
- Morally fair: There is no obvious moral issue with this method.
Conclusion: Not statistically fair.
### Situation 5:
Description: Five roommates decide who attends an event by dealing out five cards, consisting of four aces and a king. The ones dealt an ace will attend the event.
Evaluation:
- Statistically fair: Each roommate has an equal 4/5 chance of attending the event.
- Morally fair: The process gives each roommate an equal opportunity to participate without bias.
Conclusion: Both statistically and morally fair.
Based on the above evaluations:
- Situation 3 is statistically and morally fair.
- Situation 5 is statistically and morally fair.
Therefore, the correct situations are:
```markdown
[3, 5]
```
### Situation 1:
Description: A high school student decides whether to clean his room or do his homework by picking a tile at random from a bag of lettered tiles. If he picks a consonant, he will clean his room, and if he picks a vowel, he will do his homework.
Evaluation:
- Statistically fair: There are 21 consonants and 5 vowels in the English alphabet. The probability of picking a consonant is much higher (21/26) than picking a vowel (5/26). Therefore, it is not statistically fair.
- Morally fair: There are no moral issues involved.
Conclusion: Not statistically fair.
### Situation 2:
Description: Four candidates eligible for a vacancy at a company are evaluated by writing their names on pieces of paper, shuffling the papers, and drawing one at random.
Evaluation:
- Statistically fair: Each of the four candidates has an equal 1/4 chance of being selected.
- Morally fair: Ignoring qualifications and experience for a job can be considered inappropriate. It does not account for merit.
Conclusion: Not morally fair.
### Situation 3:
Description: Five cousins decide which board game to play by writing their preferred game on different sections of a spinner. The spinner has five equally-sized sections, and they will play the game written on the section where the spinner lands.
Evaluation:
- Statistically fair: Each game has exactly 1/5 chance of being selected, which is fair.
- Morally fair: All five cousins have an equal opportunity for their game to be played, so it is morally fair.
Conclusion: Both statistically and morally fair.
### Situation 4:
Description: Kate picks a tile at random from a collection of five tiles numbered 2 through 6. Kate chooses the picnic spot if she picks a prime number (2, 3, 5), and Charles chooses if Kate picks a composite number (4, 6).
Evaluation:
- Statistically fair: There are 3 prime numbers and 2 composite numbers out of the five tiles, so it is not statistically fair.
- Morally fair: There is no obvious moral issue with this method.
Conclusion: Not statistically fair.
### Situation 5:
Description: Five roommates decide who attends an event by dealing out five cards, consisting of four aces and a king. The ones dealt an ace will attend the event.
Evaluation:
- Statistically fair: Each roommate has an equal 4/5 chance of attending the event.
- Morally fair: The process gives each roommate an equal opportunity to participate without bias.
Conclusion: Both statistically and morally fair.
Based on the above evaluations:
- Situation 3 is statistically and morally fair.
- Situation 5 is statistically and morally fair.
Therefore, the correct situations are:
```markdown
[3, 5]
```
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