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Joint Probability Calculator


A
?
Ac
?
Marginal
P(B)
?
B
?
P(A∩B)
?
P(Ac∩B)
?
P(B)
?
Bc
?
P(A∩Bc)
?
P(Ac∩Bc)
?
P(Bc)
?
Marginal
P(A)
?
P(A)
?
P(Ac)
?
Total
1.000
?
How to use:
  • Direct Entry: Enter the four joint probabilities directly in the center cells. They must sum to 1.
  • From Marginals: Enter marginal probabilities (P(A), P(B)) AND one joint probability (e.g., P(A∩B)), then click "Calculate from Marginals" to compute the remaining three.
  • Auto-calculation: When you enter 2 out of 3 values in any row or column, the third is automatically calculated.
  • Complements: When you enter a marginal (e.g., P(A)), its complement (P(Ac)) is automatically calculated.

What is Joint Probability?

Joint probability measures the likelihood that two events occur together. For events A and B, P(A∩B) represents the probability that both happen simultaneously.

Key Concepts

Sample Space: All four joint probabilities represent mutually exclusive outcomes that cover the entire sample space.

Marginal Probabilities: The sum of joint probabilities across a row or column gives the probability of a single event.

Complement: P(Ac) = 1 - P(A) represents the probability that A does NOT occur.

The Law of Total Probability

The four joint probabilities partition the sample space into mutually exclusive and exhaustive events. Therefore, they must sum to exactly 1.