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Probability Calculator

Simple, complement, AND & OR probabilities โ€” decimal, percent, and fraction.

Enter probabilities as decimals between 0 and 1 (0.5 = 50%). AND/OR assume independent events.

Decimal
0.166667
Percent
16.666667%
Fraction
1/6
P = 0.166667

Step 1: P(A) = favorable รท total = 1 รท 6

Step 2: = 0.166667 = 16.666667% = 1/6

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Probability in Plain English

Probability is just favorable outcomes รท total outcomes โ€” a number between 0 (impossible) and 1 (certain). A coin flip is 0.5, a specific lottery ticket is roughly 1 in 300 million. Everything else is built from that one idea.

The Four Rules on This Page

  • Simple: P(A) = favorable รท total.
  • Complement: P(not A) = 1 โˆ’ P(A) โ€” sometimes the โ€œnotโ€ is easier to compute.
  • AND (independent): multiply โ€” P(A)ร—P(B). Two coin flips both heads: 0.5 ร— 0.5 = 0.25.
  • OR (independent): add, then subtract the overlap โ€” P(A)+P(B)โˆ’P(A)ร—P(B).

The Classic Trap

People add probabilities for AND (โ€œ10% and 10% = 20%โ€) โ€” wrong. Two independent 10% events both happening is 0.1 ร— 0.1 = 1%, not 20%. Multiplication shrinks; addition grows. When in doubt, the calculator keeps you honest.

Counting the outcomes first? Our factorial calculator handles permutations and combinations.

Frequently Asked Questions

What is the basic probability formula?

P(A) = favorable outcomes รท total outcomes. Rolling a 6 on a fair die is 1 รท 6 โ‰ˆ 0.1667, or about 16.67%.

How do you calculate AND vs OR probability?

For independent events, multiply for AND: P(A and B) = P(A) ร— P(B). For OR, use P(A or B) = P(A) + P(B) โˆ’ P(A)ร—P(B) so shared outcomes are not double-counted.

What is complement probability?

The complement is everything except the event: P(not A) = 1 โˆ’ P(A). If rain has a 25% chance, no rain has a 75% chance.

Is this probability calculator free?

Yes โ€” every tool on Math Solver Free is free with no sign-up, and all calculations run in your browser.