Using probability to make fair decisions

TL;DR

Rolling dice to decide chores is not fair, as there is a higher probability that Roberto will have to dust.

Transcript

• [Instructor] We're told that Roberto and Jocelyn decide to roll a pair of fair six-sided dice to determine who has to dust their apartment. If the sum is seven, then Roberto will dust. If the sum is 10 or 11, then Jocelyn will dust. If the sum is anything else, they'll roll again. Is this a fair way to decide who dusts? Why or why not? So pause t... Read More

Key Insights

• 🤣 Rolling two fair six-sided dice can result in 36 equally likely outcomes.
• 🤲 The probability of getting a sum of 7 is 6 out of 36, or 1/6.
• 🤲 The probability of getting a sum of 10 or 11 is 5 out of 36.
• 🤣 In any given roll, it is more likely that Roberto will have to dust than Jocelyn.
• 🧚 This method of deciding chores is not fair as there is an imbalance in the probabilities.

Questions & Answers

Q: Why do Roberto and Jocelyn decide to roll dice to determine who has to dust?

Roberto and Jocelyn want a fair way to decide who does the chores, so they use the outcome of the dice roll to make the decision.

Q: Is rolling dice to decide chores a fair method?

No, rolling dice to decide chores is not fair. The probability of getting a sum of 7, which favors Roberto, is higher than the probability of getting a sum of 10 or 11, which favors Jocelyn.

Q: What happens if the sum is neither 7, 10, nor 11?

If the sum is neither 7, 10, nor 11, they will roll the dice again. However, even on subsequent rolls, there is still a higher probability that Roberto will have to dust.

Q: Why is there a higher probability that Roberto will have to dust?

There is a higher probability that Roberto will have to dust because the outcomes that result in a sum of 7 are more than those that result in a sum of 10 or 11.

Summary & Key Takeaways

• Roberto and Jocelyn roll two fair six-sided dice to decide who will dust their apartment.

• If the sum is 7, Roberto will dust. If the sum is 10 or 11, Jocelyn will dust. Otherwise, they will roll again.

• The probability of getting a sum of 7 is 6 out of 36, while the probability of getting a sum of 10 or 11 is 5 out of 36.