Probability Calculator
Three modes for common probability problems: basic probability from outcomes, combined probability for two events (with AND/OR options), and complement probability. Useful for stats homework or just satisfying curiosity.
How to use
- For basic probability, enter how many favourable outcomes and how many total outcomes there are.
- For two events, switch to that tab and enter the probability of each event as a percentage.
- The complement tab finds P(A') - the probability that A does NOT happen.
Related tools:
Probability measures how likely an event is to occur, expressed as a number between 0 and 1 (or 0-100%). P(A) = favourable outcomes / total outcomes. A fair coin: 1/2 = 0.5. Rolling a 6 on a die: 1/6 = 0.167. These are classical probabilities where all outcomes are equally likely.
Combined probabilities follow different rules depending on whether events are independent or mutually exclusive. P(A and B) for independent events = P(A) x P(B). P(A or B) = P(A) + P(B) - P(A and B). The complement rule is P(not A) = 1 - P(A). These four rules handle most probability questions you will encounter outside a statistics course.
Frequently Asked Questions
What is the difference between independent and mutually exclusive events?
Independent events: occurrence of one does not affect the other (two coin flips). Mutually exclusive events: they cannot both occur at the same time (rolling a 2 and a 5 on one die roll). Independent events can both happen; mutually exclusive events cannot.
What is conditional probability?
P(A|B) is the probability of A given that B has already occurred. Formula: P(A|B) = P(A and B) / P(B). If 30% of students pass maths and 20% pass both maths and physics, the probability of passing physics given passing maths is 0.20/0.30 = 67%.
What is the gambler fallacy?
The mistaken belief that past independent outcomes influence future ones. If a coin lands heads 10 times in a row, the probability of the 11th being tails is still exactly 50%. Each flip is independent - the coin has no memory.