\begin{aligned} P(A|B) =\frac{P(B|A)\times P(A)}{P(B)}=\frac{P(A∩B)}{P(B)}\end{aligned}\begin{aligned} P(B|A) =\frac{P(A|B)\times P(B)}{P(A)}=\frac{P(B∩A)}{P(A)}\end{aligned}\begin{aligned} P(A∩B)=P(B∩A)\end{aligned}\begin{aligned} P(A|B) =\frac{P(B|A)\times P(A)}{P(B)}=\frac{P(A∩B)}{P(B)}\end{aligned}\begin{aligned} P(B|A) =\frac{P(A|B)\times P(B)}{P(A)}=\frac{P(B∩A)}{P(A)}\end{aligned}\begin{aligned} P(A∩B)=P(B∩A)\end{aligned}
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