If \(A\) and \(B\) are events such that \(\mathrm{P}(\mathrm{A}/\mathrm{B})=\mathrm{P}(\mathrm{B}/\mathrm{A})\neq 0\), t…

We know that, \(P\left(A∣B\right)=\frac{P(A\cap B)}{P(B)}\),

\(P\left(B∣A\right)=\frac{P(A\cap B)}{P(A)}\)

Now,

\(P\left(A∣B\right)=P\left(B∣A\right)\\ \Rightarrow \frac{P(A\cap B)}{P(B)}=\frac{P(A\cap B)}{P(A)}\)

Since \(P\left(A∣B\right)\neq 0\)\(\Rightarrow P\left(A\cap B\right)\neq 0\).

Therefore,

\(P\left(A\cap B\right)\cdot P\left(A\right)=P\left(A\cap B\right)\cdot P\left(B\right)\\ \Rightarrow P\left(A\right)=P\left(B\right)\)