Probability Calculator
Calculate probability, odds in favor, odds against, and complementary probability from favorable and total outcomes.
Probability
—
Probability (%) —
Odds In Favor —
Odds Against —
Complementary P (not event) —
Extended More scenarios, charts & detailed breakdown ▾
Probability
—
As Percentage —
Odds For —
Odds Against —
P(not event) —
Professional Full parameters & maximum detail ▾
Basic Probability
P(event) —
P(not event) —
Odds For —
Odds Against —
Binomial Distribution (n trials)
P(exactly k in n trials) —
P(at least k in n trials) —
Expected successes in n trials —
Std Dev of binomial distribution —
How to Use This Calculator
Enter the number of Favorable Outcomes (how many ways the event can occur) and Total Outcomes (all possible outcomes). The calculator shows probability, percentage, odds for, odds against, and complementary probability.
Formula
P = Favorable / Total • Odds For = Favorable:Unfavorable • P(not A) = 1 − P(A)
Example
Drawing a red card from a deck: 26/52 = 0.5 = 50%, Odds 1:1
Frequently Asked Questions
- Probability is a numerical measure of how likely an event is to occur, expressed as a number between 0 and 1 (or 0% to 100%). Formula: P(event) = number of favorable outcomes / total number of equally likely outcomes. For example, flipping a fair coin: P(heads) = 1/2 = 0.5 = 50%. A probability of 0 means the event is impossible; a probability of 1 (100%) means it is certain. Probabilities of all possible outcomes must sum to 1. This classical definition assumes equally likely outcomes — for unequal cases, use empirical (frequency-based) probability.
- Probability and odds both describe likelihood but in different ways. Probability = favorable / total outcomes. Odds in favor = favorable : unfavorable outcomes. Example: drawing an ace from a deck. P(ace) = 4/52 = 1/13 ≈ 7.7%. Odds in favor = 4:48 = 1:12. Odds against = 48:4 = 12:1. To convert probability to odds: if P = 1/13, odds in favor = 1:(13−1) = 1:12. To convert back: P = favorable / (favorable + unfavorable) = 1 / (1+12) = 1/13. Sports betting uses odds extensively.
- The complementary probability is the probability that an event does not occur: P(not A) = 1 − P(A). For example, if P(rain today) = 0.3, then P(no rain) = 1 − 0.3 = 0.7. This rule is especially useful when the direct probability is harder to compute than its complement. For example, P(at least one head in 3 flips) = 1 − P(no heads) = 1 − (1/2)³ = 1 − 1/8 = 7/8 ≈ 87.5%. The complement rule always holds: P(A) + P(not A) = 1.
- Two events A and B are independent if the occurrence of one does not affect the probability of the other. For independent events: P(A and B) = P(A) × P(B). Example: flipping a coin and rolling a die are independent. P(heads and 6) = 1/2 × 1/6 = 1/12. In contrast, dependent events (like drawing cards without replacement) require conditional probability: P(A and B) = P(A) × P(B|A). A common misconception is the "gambler's fallacy" — assuming past independent outcomes affect future ones, which they do not.
- On a fair six-sided die, there is 1 favorable outcome (rolling a 6) out of 6 equally likely outcomes (1, 2, 3, 4, 5, 6). Therefore P(6) = 1/6 ≈ 0.1667 = 16.67%. The odds in favor of rolling a 6 are 1:5 (one way to succeed, five ways to fail). For rolling at least one 6 in two rolls: P = 1 − P(no 6 in 2 rolls) = 1 − (5/6)² = 1 − 25/36 = 11/36 ≈ 30.6%. Enter favorable = 1, total = 6 in this calculator to confirm the single-roll result.