Enter the number of favorable outcomes and total outcomes to compute the probability of a single event — or switch to two-event mode to compute joint and union probabilities for independent or mutually exclusive events.
How to use this calculator
Single event: enter favorable outcomes and total outcomes to get P(A), complement, and odds.
Two events: enter P(A) and P(B) and select whether they are independent or mutually exclusive to get P(A and B) and P(A or B).
Formula & method
Basic probability formulas
P(A) = favorable / total · P(not A) = 1 − P(A) · P(A ∩ B) = P(A) × P(B) (independent) · P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
All probabilities must lie in [0, 1].
Example
Rolling a 3 on a fair die: P(3) = 1/6 ≈ 0.167, P(not 3) = 5/6 ≈ 0.833, Odds = 1:5.
Key insights
Probability ranges from 0 (impossible) to 1 (certain).
P(not A) = 1 − P(A). The complement rule is the fastest way to handle 'at least one' problems.
For independent events: P(A and B) = P(A) × P(B).
For mutually exclusive events: P(A and B) = 0, P(A or B) = P(A) + P(B).
How to interpret your result
Odds vs probability
Probability P(A) = favorable/total. Odds in favour = favorable:unfavorable. Odds 1:5 = P(A) = 1/6 ≈ 0.167.
Independent vs mutually exclusive
Independent: one event does not affect the other (coin flips). Mutually exclusive: both cannot occur simultaneously (rolling a 2 or a 5 on one die).
Frequently asked questions
What is probability?
Probability P(A) = favorable outcomes / total outcomes. It measures how likely an event is, ranging from 0 (impossible) to 1 (certain).
What is the complement rule?
P(not A) = 1 − P(A). Used for 'at least one' problems: P(at least one A in n trials) = 1 − P(none).
What are independent events?
Events where one outcome does not influence the other. P(A and B) = P(A) × P(B).
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