Let's analyze each situation to determine if it is both statistically fair and appropriate for the decision to be left up to chance.
### Situation #1:
A high school student is deciding whether to first clean his room or do his homework by picking a random tile 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.
- Analysis: This decision does not have severe consequences, and it can be reasonably left up to chance. Choosing between cleaning a room or doing homework has a minor impact, and both tasks need to be done eventually. Using a random tile to decide is fair and does not create an imbalance in outcome.
Conclusion: Statistically fair.
### Situation #2:
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.
- Analysis: This situation involves making a significant decision that should be based on merit, qualifications, and experience. Ignoring these critical factors and making the decision by random drawing is not fair and does not preserve the integrity of the hiring process. It opposes meritocracy.
Conclusion: Not statistically fair.
### Situation #3:
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.
- Analysis: Deciding on a board game is a minor decision and fits well into a simple chance selection method. All cousins have an equal opportunity, and the outcome is unlikely to cause any significant issues. Using a spinner is a fair and equitable way to decide.
Conclusion: Statistically fair.
### Situation #4:
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 specific number.
- Analysis: This situation is similar to randomly deciding a simple preference among a group. Determining who picks the picnic spot can reasonably be left to chance without significant consequences. Each tile represents an equal opportunity.
Conclusion: Statistically fair.
### Summary:
The situations that are statistically fair and appropriate for a decision to be left up to chance are:
- Situation #1
- Situation #3
- Situation #4
Therefore, the correct situations are:
[tex]\[ [1, 3, 4] \][/tex]
