Probability Calculator
Three probability calculators: a single event from favorable and total outcomes, two independent events combined with AND or OR, and the complement of an event. Probabilities can be entered as decimals, percentages, or fractions, and every formula is worked through with your numbers.
Single event
P = 0.1667 (16.6667%)
P(event) = favorable ÷ total = 1 ÷ 6 = 0.1667
As a percentage: 0.1667 × 100 = 16.6667%
Odds in favor: 1 favorable to 5 unfavorable = 1 : 5
Two independent events — AND / OR
P(A and B) = 0.0833 (8.3333%)
P(A and B) = P(A) × P(B)
= 0.5 × 0.1667 = 0.0833
P(A or B) = 0.5833 (58.3333%)
P(A or B) = P(A) + P(B) − P(A) × P(B)
= 0.5 + 0.1667 − 0.0833 = 0.5833
Honest note: these formulas assume A and B are independent — one happening does not change the other's probability. For dependent events (like drawing cards without replacement) they do not apply.
Complement — P(not A)
P(not A) = 0.7 (70%)
P(not A) = 1 − P(A)
= 1 − 0.3 = 0.7
Frequently Asked Questions
- How do I calculate the probability of a single event?
- Divide the number of favorable outcomes by the total number of equally likely outcomes. Rolling a 6 on a fair die is 1 ÷ 6 ≈ 0.1667, or about 16.67%.
- How do I calculate the probability of two events both happening?
- For independent events, multiply the individual probabilities: P(A and B) = P(A) × P(B). Two coin flips both landing heads is 0.5 × 0.5 = 0.25.
- How do I calculate the probability of A or B?
- For independent events, P(A or B) = P(A) + P(B) − P(A) × P(B). The subtraction removes the overlap where both happen, so it is not counted twice.
- What is a complement in probability?
- The complement of an event is it not happening: P(not A) = 1 − P(A). If rain has a 30% probability, no rain has a 70% probability.
- What does "independent events" mean?
- Two events are independent when one happening does not change the probability of the other, like two separate coin flips. The AND and OR formulas on this page assume independence — they give wrong answers for dependent events, such as drawing cards without replacement.
- What is the difference between probability and odds?
- Probability is favorable outcomes over all outcomes; odds compare favorable to unfavorable outcomes. A 1-in-6 chance is a probability of 1/6 but odds of 1:5 in favor.