List of top Mathematics Questions on Bayes' Theorem asked in KCET

Meera visits only one of the two temples $A$ and $B$ in her locality. Probability that she visits temple $A$ is $\dfrac{2}{5}$. If she visits temple $A$, $\dfrac{1}{3}$ is the probability that she meets her friend, whereas it is $\dfrac{2}{7}$ if she visits temple $B$. Meera met her friend at one of the two temples. The probability that she met her friend at temple $B$ is:

Events $E_1$ and $E_2$ from a partition of the sample space S. A is any event such that $P(E_1) = P(E_2) = \frac{1}{2}, P(E_2/A) = \frac{1}{2}$ and $P(A/E_2)=\frac{2}{3}$, then $P(E_1/A) $ is