Question

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.
Situation #1 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.
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.
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.
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 prime number, and Charles chooses if Kate picks a composite number.
Situation #5 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.
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Answer 1

The situations that are both statistically fair and morally fair are Situation 2, Situation 3 and Situation 5

How to categorize the situations?

For a situation to be fair, the probability of every outcome must be equal.

We can now analyze each option using the above highlight

Situation 1

• Alphabets = 26
• Probability of vowel = 5/26
• Probability of consonant = 21/26

The probabilities of vowels and consonant are not equal.

Hence, this situation is not fair

Situation 2

People = 4

P(Each) = 1/4

The probability of each participant is equal in the above scenario i.e. 1/4

Hence, this situation is fair

Situation 3

• People = 5
• P(Each) = 1/5

The probability of each cousin is equal in the above scenario i.e. 1/5

Hence, this situation is fair

Situation 4

• Numbers = 5 i.e. 2 to 6
• P(Prime) = 3/5
• P(Composite) = 4/6

The probabilities of prime and composite numbers are not equal.

Hence, this situation is not fair

Situation 5

• Roommates = 5
• Cards = 5
• Aces = 4
• P(Each) = 1/5

All probabilities are equal in the above scenario i.e. 1/5

Hence, this situation is fair

Read more about probability at:

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