Answered

Select all the correct situations in the table.

Based on probability and if it is appropriate for a decision to be left up to chance, choose every situation that is both statistically fair and morally fair.

\begin{tabular}{|l|l|}
\hline
Situation \#1 & \begin{tabular}{l}
A high school student is deciding whether to first clean his room or do his homework. \\
He decides 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.
\end{tabular} \\
\hline
Situation \#2 & \begin{tabular}{l}
There are four candidates eligible for a vacancy at a company. Ignoring qualifications \\
and experience, the recruitment manager decides which candidate to hire by writing \\
their names on pieces of paper, shuffling the papers, and drawing one at random.
\end{tabular} \\
\hline
Situation \#3 & \begin{tabular}{l}
Five cousins are deciding which board game to play. They each write their preferred \\
game on a different section of a spinner that has five equally-sized sections. They \\
spin the spinner and will play the game written on the section where the spinner \\
lands.
\end{tabular} \\
\hline
Situation \#4 & \begin{tabular}{l}
To determine who can choose the spot for a picnic, Kate picks a tile at random from a \\
collection of five tiles, numbered 2 through 6. Kate chooses the spot if she picks a \\
prime number, and Charles chooses if Kate picks a composite number.
\end{tabular} \\
\hline
Situation \#5 & \begin{tabular}{l}
Five roommates all want to attend an event, but they only have four invites. To decide \\
who will attend, they shuffle a set of five cards consisting of four aces and a king. \\
Each roommate is randomly dealt a card. The ones dealt an ace will attend the event.
\end{tabular} \\
\hline
\end{tabular}



Answer :

GinnyAnswer
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]
```