If $E_1$ and $E_2$ are equally likely, mutually exclusive and exhaustive events and $P(A|E_1) = 0.2$, $P(A|E_2) = 0.3$, then $P(E_1|A)$ is equal to...

Let $U_1$ and $U_2$ be two urns such that $U_1$ contains $3$ white and $2$ red balls,and $U_2$ contains only $1$ white ball. $A$ fair coin is tossed. If it shows head,$1$ ball is drawn at random from $U_1$ and transferred to $U_2$. If it shows tail,$2$ balls are drawn at random from $U_1$ and transferred to $U_2$. Now,$1$ ball is drawn at random from $U_2$. Given that the ball drawn from $U_2$ is white,what is the probability that the coin showed head?

An urn contains $5$ balls. Two balls are drawn at random and they are found to be white. The probability that all the balls in the urn are white is:

The probability of men getting a certain disease is $\frac{1}{2}$ and that of women getting the same disease is $\frac{1}{5}$. The blood test that identifies the disease gives the correct result with probability $\frac{4}{5}$. Suppose a person is chosen at random from a group of $30$ males and $20$ females,and the blood test of that person is found to be positive. What is the probability that the chosen person is a man?

$A$ family consists of $8$ persons. If $4$ persons are chosen at random and they are found to be $2$ men and $2$ women,then the probability that there are equal number of men and women in that family is

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