Calculate the probability of a simple event from favorable and total outcomes.
P(event) = favorable outcomes ÷ total possible outcomes.
The single most important question in any probability calculation involving multiple events is whether they're independent or dependent — and getting this wrong is the most common source of probability mistakes. Independent events don't affect each other's odds: two separate coin flips are independent, so the probability of getting heads twice in a row is simply the two individual probabilities multiplied together (1/2 × 1/2 = 1/4). Dependent events do affect each other: drawing two cards from a deck without replacement is dependent, because removing the first card changes the composition of the deck (and therefore the odds) for the second draw — the probability of drawing two aces in a row from a standard deck is 4/52 × 3/51, not 4/52 × 4/52, because only 3 aces remain among 51 cards after the first is removed.
A related, equally common trap is confusing "and" with "or" — the probability of two independent events both happening ("and") multiplies their individual probabilities, while the probability of at least one of two events happening ("or") generally requires adding the probabilities and then subtracting the probability of both happening together, to avoid double-counting the overlap. This overlap-correction step is easy to forget, and skipping it is exactly what produces probabilities that come out too high — sometimes even exceeding 100%, a clear sign the calculation missed the overlap between the two events being combined.
Independent events don't affect each other's odds — like separate coin flips, where each flip's probability stays the same regardless of previous results. Dependent events do affect each other — like drawing cards without replacement, where removing one card changes the odds for the next draw.
Multiply their individual probabilities together. Two independent coin flips both landing heads: 1/2 × 1/2 = 1/4. This 'and' rule for independent events is one of the most frequently used probability calculations.
Because drawing without replacement makes the two draws dependent — after removing one ace from the deck, only 3 aces remain among the 51 remaining cards. The correct calculation is 4/52 × 3/51, accounting for how the first draw changes the odds for the second.
Because simply adding the two individual probabilities double-counts the outcomes where both A and B happen together. The correct formula is P(A or B) = P(A) + P(B) − P(A and B), subtracting that overlap once so it isn't counted twice — skipping this step is what produces impossible probabilities exceeding 100%.