Joint Probability Calculator

Combine the probabilities of two independent events.

How the Math Works

The Joint Probability Calculator uses fundamental probability rules for independent events. When two events A and B are independent, the probability both occur together is found by multiplying their individual probabilities: P(A∩B) = P(A)·P(B). For the probability of either event occurring, we use the inclusion-exclusion principle: P(A∪B) = P(A) + P(B) - P(A∩B). This accounts for the overlap where both events might happen simultaneously, preventing double-counting.

Practical Applications

To use this calculator, first determine if your events are independent - meaning the occurrence of one doesn't affect the probability of the other. Enter P(A) and P(B) as decimal values between 0 and 1. The calculator then multiplies them to find the joint probability and applies the inclusion-exclusion formula to determine the union probability. For example, if there's a 30% chance of rain tomorrow (P(A) = 0.3) and a 40% chance of traffic delays (P(B) = 0.4), you can find the probability of both occurring or either occurring.

Day-to-Day Use

Understanding joint probabilities helps you assess combined risks in everyday decisions. When planning a trip, you might calculate the probability of both flight delays and weather disruptions before choosing your departure time. In health contexts, you could determine the likelihood of experiencing multiple side effects from different medications. Financial decisions also benefit - you might calculate the joint probability of investment losses across different sectors to diversify your portfolio. This knowledge builds better risk awareness for everything from travel planning to medical decisions.

Worked example

50% & 40% → AND 20%, OR 70%.

FAQ