Compound Probability Calculator

Enter the probability of event A occurring and the probability of event B occurring into the compound probability calculator. The calculator will display the probability of both events happening.

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Compound Probability Formula

The following formula is used to calculate the probability of both events A and B occurring (the intersection).

\begin{aligned}
P(A \cap B) &= P(A)\cdot P(B\mid A) \\
&= P(B)\cdot P(A\mid B) \\
\text{If A and B are independent: } \; P(A \cap B) &= P(A)\cdot P(B)
\end{aligned}

• Where P(A ∩ B) is the probability of both events A and B occurring
• P(A) is the probability of event A
• P(B) is the probability of event B
• P(B|A) is the probability of event B occurring given that event A has occurred

For independent events, you can calculate the probability of both events happening by multiplying P(A) and P(B). For dependent events, use the conditional probability P(B|A) (or P(A|B)).

Compound Probability Definition

A compound probability is the probability of two (or more) events considered together, such as “A and B” (both occur) or “A or B” (at least one occurs). For “A and B,” the probability of both events occurring is P(A ∩ B), which is found using P(A)·P(B|A). If A and B are independent, then P(B|A)=P(B) and the formula simplifies to P(A)·P(B). Probabilities can be entered as decimals or percentages as long as you use consistent units (for example, convert 25% to 0.25 when working in decimals).

How to calculate compound probability?

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