Glossary term
Mutually Exclusive
Two outcomes are mutually exclusive when they cannot both happen at once, so at most one of them occurs.
Visual intuition
50%
0
EV
5
50%
10
Each play pays 0 or 10 — never both
One play lands on exactly one ticket: 0 or 10, never both at once. Mutually exclusive outcomes like these are why the two 50% chances account for everything — and why the wheel can average them into a single expected value.
Formula
P(A or B) = P(A) + P(B), when A and B cannot both happen
Example
A card cannot be both a heart and a spade — mutually exclusive — so P(heart or spade) = 13/52 + 13/52 = 1/2; hearts and queens overlap, so those two probabilities cannot simply be added.
How It Works
One play pays either 0 or 10 — never both. Outcomes that cannot co-occur are mutually exclusive, and that is what licenses adding probabilities: the of this-or-that is the chance of this plus the chance of that (a die shows 1, 2, or 3 with probability 1/6 + 1/6 + 1/6 = 1/2). The classic mix-up is with , but the two are near opposites: mutually exclusive events are maximally dependent — if one happened, the other's probability just crashed to zero. And the addition shortcut breaks the moment outcomes can overlap: 'rain on Saturday or Sunday' can be both, so those chances cannot simply be added.
Concepts
Conditional Probability
The probability of something after new information changes what is still possible. The important move is to update the denominator: cases ruled out by the new information should no longer be counted. Many mistakes happen when people keep using the original odds after the situation has narrowed.
Expected Value
The long-run average outcome: each result weighted by how likely it is. It tells you whether a bet is favourable on average, but it ignores how badly a single rare outcome would hurt — which is why people rationally pay to avoid losses they could not absorb.
