Probability rules
For two independent events, where one happening doesn't change the chance of the other (like two coin flips):
Example: with P(A) = 0.5 and P(B) = 0.4, the chance of both is 0.2, of at least one is 0.5 + 0.4 − 0.2 = 0.7, and of neither is 0.5 × 0.6 = 0.3. The chance A happens at least once in 3 tries is 1 − 0.5³ = 87.5%.
Common mistakes
- Adding probabilities for "at least once". A 1-in-6 chance over 6 rolls isn't 100%; it's 1 − (5/6)⁶ = 66.5%.
- The gambler's fallacy. Independent events have no memory: after five heads, the next flip is still 50%.
- Assuming independence. Drawing cards without putting them back changes the odds each time, so these formulas don't apply directly.
Odds and probability are different ways to say the same thing: a 20% chance is odds of 1 to 4. For random draws, try the random number generator.
Frequently asked questions
How do you calculate the probability of two events?
If they're independent, multiply for "and" (both happen) and use P(A) + P(B) − P(A)P(B) for "or" (at least one happens).
What is the probability of something happening at least once?
Take the chance it doesn't happen in one try, raise it to the number of tries, and subtract from 1: 1 − (1 − p)ⁿ.
What is the difference between odds and probability?
Probability compares successes to all outcomes; odds compare successes to failures. A probability of 0.25 is 1 success to 3 failures, or odds of 1 to 3.
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