Assuming outcomes are equally likely when they are not
"The Fair Fallacy"
The Mistake in Action
There are 3 options: win, lose, or draw. Find P(win).
Student writes: "P(win) = 1/3"
Why It Happens
Students see three outcomes and assume each has equal probability, when the question hasn't stated this. Real-world outcomes are often not equally likely.
The Fix
Only use $\frac{1}{n}$ if outcomes are EQUALLY LIKELY (fair dice, fair coin, etc.)
If the question doesn't say "fair" or "equally likely", you need more information.
For a football match, win/lose/draw are NOT equally likely — they depend on the teams!
Ask yourself: "Does the question tell me these outcomes are equally likely?" If not, you can't assume they are.
Spot the Mistake
Can you identify where this student went wrong?
Outcomes: win, lose, draw (3 outcomes)
P(win) = 1/3
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: