From a group of $8$ boys and $3$ girls,a committee of $5$ members is to be formed. Find the probability that $2$ particular girls are included in the committee.

$A$ coin is tossed three times in succession. If $E$ is the event that there are at least two heads and $F$ is the event in which the first throw is a head,then $P(E|F) = $

$A$ candidate takes three tests in succession and the probability of passing the first test is $p$. The probability of passing each succeeding test is $p$ if he passes the preceding one, and $\frac{p}{2}$ if he fails the preceding one. The candidate is selected if he passes at least two tests. The probability that the candidate is selected is:

Let $A$ and $B$ be two events such that $P(A) = \frac{5}{11}$, $P(B) = \frac{2}{11}$, and $P(A \cup B) = \frac{3}{11}$, then $P(A'|B')$ is . . . . . . .

If $P(A)=0.8, P(B)=0.5$ and $P(B | A)=0.4,$ find $P(A \cap B).$

If $C$ and $D$ are two events such that $P(D) \neq 0$,then which of the following statements is correct?