University AI - Bayes Theorem

Bayes Theorem

$$\begin{array}{rl}1.& P(A,B)=P(B,A)\\ 2.& P(A,B)=P(A)\cdot P(B|A)\\ & P(B,A)=P(B)\cdot P(A|B)\\ 3.& P(A|B)=\frac{P(A)}{P(B)}P(B|A)\end{array}$$

Where:

• $P(A|B)$ is the conditional probability (a pdf) of the event $A$ happening in case of being in the condition of $B$, for example: $A=$ probability of picking a girl in a crowd $B=$ being in a engineering university $P(A)=0.51$ (we consider the more general case, in the world the percentage of female is $52\%$ and of males is $48\%$ ) $P(A|B)=0.20$ (in an engineering course the percentage of females is around $20\%$)

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