Math
Probability Calculator
Calculate single, combined, and conditional probabilities with odds and complements.
Pick a probability question
Enter each probability as a decimal between 0 and 1 (for example, 0.25 means a 25 percent chance).
P(A)
0.5
50%
- Complement
- 0.5
- Odds for
- 1:1
- Odds against
- 1:1
Probability of event A.
Frequently Asked Questions about the Probability Calculator
What is probability?
Probability is a number between 0 and 1 that measures how likely an event is. 0 means the event cannot happen, 1 means it is certain, and 0.5 means a 50% chance - like a fair coin flip. Enter any value in that range and the calculator converts it to a percentage and odds ratio for you.
How do I calculate P(A and B) for independent events?
Multiply the two probabilities: P(A and B) = P(A) x P(B). This formula only holds when the events are independent - meaning the outcome of one does not affect the other. For example, rolling a 6 on a die (1/6) and flipping heads (1/2) gives P(both) = 1/12, about 8.33%.
How do I calculate P(A or B)?
The calculator uses P(A or B) = P(A) + P(B) - P(A) x P(B). Subtracting the joint probability prevents counting the overlap twice. If P(A) = 0.3 and P(B) = 0.4, then P(A or B) = 0.3 + 0.4 - 0.12 = 0.58, or 58%.
What is conditional probability?
P(A|B) is the probability of A given that B has already occurred. The calculator computes it as P(A and B) / P(B), which requires P(B) > 0 and P(A and B) <= P(B). For example, if P(A and B) = 0.1 and P(B) = 0.4, then P(A|B) = 0.25, or 25%.
How do odds relate to probability?
Odds express the ratio of favorable outcomes to unfavorable ones. The calculator reduces this to the lowest integer ratio using the greatest common divisor. A probability of 0.25 (25%) becomes odds of 1:3 in favor - one favorable outcome for every three unfavorable ones. To go the other way: if odds are 1:3, probability = 1 / (1 + 3) = 0.25.