If $A$ and $B$ are two events such that $P(B) \neq 0$ and $P(B) \neq 1$,then $P(\bar{A} \mid \bar{B})$ is equal to:

Find $P(E | F)$ when two coins are tossed once,where $E$ is the event that a tail appears on one coin,and $F$ is the event that one coin shows a head.

If $A$ and $B$ are two events such that $A \subset B$ and $P(B) \neq 0$,then which of the following is correct?

Given $P(A)=0.5, P(B)=0.4, P(A \cap B)=0.3$,then $P(A^{\prime} / B^{\prime})$ is equal to

Let $S$ be the sample space of all $3 \times 3$ matrices with entries from the set $\{0, 1\}$. Let the events $E_1$ and $E_2$ be given by $E_1 = \{A \in S : \operatorname{det} A = 0\}$ and $E_2 = \{A \in S : \text{sum of entries of } A \text{ is } 7\}$. If a matrix is chosen at random from $S$,then the conditional probability $P(E_1 \mid E_2)$ equals:

$A$ couple has two children. If at least one of them is a boy,then the probability that the other is also a boy is: