For a single event, you enter favorable and total outcomes; the tool divides to get P(A) and subtracts from 1 for the complement. For two independent events, it multiplies probabilities for "and," adds them minus the overlap for "or," and divides for the conditional. The coin flip tab uses the binomial coefficient C(n, k) × 0.5ⁿ to compute the exact probability. All tabs assume events are independent — dependent events require conditional probability adjustments not covered here.
Two events are independent if the outcome of one doesn't affect the other. Flipping two coins is independent — the first flip doesn't change the odds of the second. Drawing cards without replacement is dependent because the deck changes after each draw.
Without the subtraction, you'd double-count outcomes where both events happen. The inclusion-exclusion formula P(A or B) = P(A) + P(B) − P(A and B) corrects for this overlap.
Yes. The coin flip tab assumes exactly 50% heads and 50% tails on each flip. For a biased coin, you'd need a generalized binomial formula with a different probability parameter.
The calculator uses JavaScript's built-in number precision, which limits accuracy for factorials beyond about 170. For typical use (under 50 flips), results are exact. Very large values may lose precision.
Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.