Is the chance equal for everyone?
Be able to determine if a situation gives everyone the same chance and justify this using outcomes.
Prerequisites
Everyday explanation
A situation is fair when everyone has an equal chance of winning.
Example: You and a colleague draw lots to decide who takes the first meeting. You win on 1, 2, 3. Your colleague wins on 4, 5, 6. → Three outcomes out of six. Fair.
Example: You win on even numbers (2, 4, 6), your colleague wins on 6. → You have 3 out of 6, your colleague has 1 out of 6. Unfair.
The way to decide: count how many outcomes result in a win for each person, out of all possible outcomes.
Interactive
A tricky scenario: Roll two dice and add them up. You win if the sum is 7. Your colleague wins if the sum is 2 or 12.
Does that sound fair? “One number versus two numbers.” But count the outcomes out of 36:
- Sum 7: (1,6) (2,5) (3,4) (4,3) (5,2) (6,1) = 6 ways
- Sum 2: (1,1) = 1 way. Sum 12: (6,6) = 1 way → 2 ways
You win three times as often. Counting ways, not numbers, is the whole point.
Simulate 30 rounds and see if reality matches the calculation.
Mastery means
- Counts the outcomes for each party
- Determines if a situation is fair and proposes a change
Sign in to do the exercises and build your mastery up.
Sources
- CS Unplugged (CC BY-SA 4.0) — CC BY-SA 4.0
- Wikipedia — Sannolikhet (CC BY-SA 4.0) — CC BY-SA 4.0