Probability calculator
The core probability identities, evaluated at once so you can see how they relate.
%
%
%
Probability of A or B
58.0000%
- Probability of neither
- 42.0000 %
- Probability of A given B
- 30.0000 %
- Probability of B given A
- 40.0000 %
- Probability of A but not B
- 18.0000 %
- What both would be if independent
- 12.0000 %
Show the working
- Probability of A = 30
- Probability of B = 40
- Probability of both = 12
- a = 30 / 100 = 0.3
- b = 40 / 100 = 0.4
- both = 12 / 100 = 0.12
- Probability of A or B = (0.3 + 0.4 - 0.12) * 100 = 58
- Probability of neither = 100 - 58 = 42
- Probability of A given B = 0.4 > 0 ? 0.12/0.4*100 : 0 = 30
- Probability of B given A = 0.3 > 0 ? 0.12/0.3*100 : 0 = 40
- What both would be if independent = 0.3 * 0.4 * 100 = 12
- Probability of A but not B = (0.3 - 0.12) * 100 = 18
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- P(A or B) = P(A) + P(B) - P(A and B)
- P(A | B) = P(A and B) / P(B)
- A and B are independent when P(A and B) = P(A) P(B)
If the "both" figure equals the independent product, the two events are independent.