Calculated using standard mathematical and industry formulas.
Free online Probability Calculator calculator for academic, engineering, and statistical math.
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 & calculation 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].
Step-by-step calculation 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 to remember
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 results?
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
How does the Probability Calculator calculator work?
It uses standard algebraic, geometric, or statistical theorems to return exact values.
How accurate are the results?
All calculations use double-precision floating-point arithmetic for exact accuracy.
Can I copy the step-by-step work?
Yes, step-by-step solutions are formatted clearly for homework or documentation.
How are undefined operations handled?
The calculator flags mathematical errors such as division by zero or negative square roots.
Is this tool suitable for students and engineers?
Yes, it is designed for students, teachers, engineers, and scientists.
Does it support negative numbers and decimals?
Yes, all real numbers (positive, negative, fractions, and decimals) are supported.
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