## 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 $i=1,2,\cdots , n$.