## Bayes’ Probability Calculator

Bayes Probability Calculator
Event $P(A_k)$ $P(B|A_k)$
Event $A_1$
Event $A_2$
Results
Total Probability $P(B)$
$P(A_1|B)$
$P(A_2|B)$

## Formula

\begin{aligned} P(A|B) &=\frac{P(A)P(B|A)}{P(B)}\\ &= \frac{P(A)P(B|A)}{P(A)P(B|A)+P(A^\prime)P(B|A^\prime)} \end{aligned}

For more than one event:

Let $A_1, A_2, \cdots, A_n$ are mutually exclusive and exhaustive events of the sample space $S$ and if $P(A_i)\neq 0$, $i=1,2,\cdots,n$, then for any event $B$ of the sample space $S$

$$\begin{equation*} P(A_i/B) =\frac{P(A_i) A(B/A_i)}{\sum_{i=1}^n P(A_i) A(B/A_i)} \end{equation*}$$ for $i=1,2,\cdots , n$.