Joint Probability Calculator

What Is Joint Probability?

Joint probability measures the likelihood that two events occur together. For independent events, the joint probability is the product of individual probabilities. For dependent events, use the conditional probability of one event given the other. Explore related tools like the Conditional Probability Calculator and Probability Calculator.

Joint Probability Formulas

For independent events A and B:

$$P(A \cap B) = P(A) \times P(B)$$

For dependent events:

$$P(A \cap B) = P(A) \times P(B \mid A)$$

Example: Exam Pass Rates

A student has an 80% chance of passing math and a 60% chance of passing science. If the exams are independent, the joint probability of passing both is $0.8 \times 0.6 = 0.48$, or 48%.

Frequently Asked Questions

What is the difference between independent and dependent events?

Independent events do not affect each other's outcomes. Dependent events influence each other's likelihoods, so you must use conditional probability P(B | A) instead of P(B).

Can joint probability be greater than 1?

No. All probabilities, including joint probabilities, must be between 0 and 1. Values outside this range are invalid.

How do I calculate joint probability for dependent events?

Multiply P(A) by P(B | A), the probability of B occurring given that A has already occurred. For example, if P(A) = 0.8 and P(B | A) = 0.7, then P(A and B) = 0.56.

When should I use independent vs dependent mode?

Use independent mode when one event does not change the probability of the other, such as flipping two fair coins. Use dependent mode when outcomes are linked, such as drawing cards without replacement.

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