Probability Calculator
Single events, AND, OR, and complements — every answer as a reduced fraction, a decimal, and a percent, in plain English.
P = favorable outcomes ÷ total outcomes. Example: rolling a 6 on a die → 1 favorable, 6 total.
P(A and B) = P(A) × P(B). Only for independent events — one must not affect the other.
P(A or B) = P(A) + P(B). Only when both can’t happen at once (mutually exclusive).
P(A or B) = P(A) + P(B) − P(both). Use when the events can overlap.
P(not A) = 1 − P(A). The shortcut when “not happening” is easier to think about.
Step-by-step
How to use the probability calculator
- Pick a mode. One event? “Single event.” Both happening? “AND.” Either happening? “OR” — exclusive if they can’t overlap, general if they can. The opposite of an event? “Complement.”
- Enter your numbers. Counts for single events; decimals between 0 and 1 for the rest.
- Press Calculate. You get the reduced fraction, the decimal, and the percent — plus a plain-English verdict like “roughly 1 in 4.”
- Check the steps. Each line substitutes your numbers into the rule, so you can copy the working.
- Watch the traps. AND needs independent events; exclusive OR needs totals under 100%; and P(both) can never exceed either event.
Frequently asked questions
What is probability, exactly?
The number of favorable outcomes divided by the total number of possible outcomes. A fair coin landing heads: 1 favorable outcome out of 2 possible, so P = 1/2 = 0.5 = 50%.
When do you add vs. multiply probabilities?
Multiply for AND (both events happen): P(A and B) = P(A) × P(B) for independent events. Add for OR with mutually exclusive events (can’t both happen): P(A or B) = P(A) + P(B). If they can overlap, subtract P(both) so you don’t double-count.
What are independent events?
Events where one doesn’t affect the other — like two coin flips. P(heads AND heads) = 1/2 × 1/2 = 1/4. If the first event changes the odds of the second (drawing cards without replacing), they’re dependent and you can’t just multiply the starting probabilities.
What is the complement rule?
P(event happens) = 1 − P(event doesn’t happen). It’s the shortcut when “not happening” is easier: the chance of at least one head in 3 flips is 1 − P(no heads) = 1 − 1/8 = 7/8.
Can a probability be more than 1?
No — probabilities live between 0 (impossible) and 1 (certain), inclusive. If your numbers give more than 1, something’s off: check that favorable ≤ total, or that your “or” events don’t overlap more than you accounted for.
More from the codex
Probability Calculator
Single events, AND, OR, and complements — fraction, decimal, percent.
LCM & GCF Calculator
GCF, LCM, and prime factorization of up to 6 numbers.
Open tool → LivePrime Factorization Calculator
Factor any integer up to a trillion, step by step.
Open tool → LivePermutation & Combination Calculator
nPr and nCr, with or without repetition.
Open tool →Questions or feedback?
Found a bug or want a feature? Email [email protected] — every message is read by the indie dev behind the codex.