Probability Calculator
For any two events P(A or B) = P(A) + P(B) − P(A and B): independent events with probabilities 0.5 and 0.4 give 0.7.
A probability from 0 to 1 (0.25, not 25 %).
0.7
- P(A and B)
- 0.2
- P(not A)
- 0.5
- P(not B)
- 0.6
- P(neither A nor B)
- 0.3
- P(A given B) = P(A and B)/P(B)
- 0.5
- P(B given A)
- 0.4
Step-by-step solution
- Independent: P(A and B) = P(A)·P(B) = 0.5 × 0.4 = 0.2
- P(A or B) = P(A) + P(B) − P(A and B) = 0.5 + 0.4 − 0.2 = 0.7
Probability Formula
P(A or B) = P(A) + P(B) − P(A and B)
independent: P(A and B) = P(A)P(B); P(A|B) = P(A and B)/P(B)
Worked Example
Independent events with P(A) = 0.5 and P(B) = 0.4:
- Independent: P(A and B) = P(A)·P(B) = 0.5 × 0.4 = 0.2
- P(A or B) = P(A) + P(B) − P(A and B) = 0.5 + 0.4 − 0.2 = 0.7
P(not A): 0.5 · P(not B): 0.6 · P(neither A nor B): 0.3 · P(A given B) = P(A and B)/P(B): 0.5 · P(B given A): 0.4
Test-day tip
Most SAT probability questions use a two-way table. Read the condition (“given that…”) first to pick the right denominator, then the count you want.
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Frequently asked questions
How do I read conditional probability from a two-way table?
Restrict to the given row or column: P(A | B) = (count in both A and B) ÷ (total count in B).
What is the difference between independent and mutually exclusive?
Independent events do not affect each other (P(A and B) = P(A)P(B)); mutually exclusive events cannot happen together (P(A and B) = 0).
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Probability Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/probability-calculator/
IEEE
Scientific Converters, "Probability Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/probability-calculator/