One card is drawn at random from a well-shuffled pack of $52$ cards. The probability that the card drawn is a face card (Jack,Queen,and King only) is

Mr. $A$ has six children and at least one child is a girl. Then,the probability that Mr. $A$ has $3$ boys and $3$ girls is:

$A$ student appears for tests $I$, $II$, and $III$. The student is successful if they pass in tests ($I$ and $II$) $OR$ ($I$ and $III$). The probabilities of the student passing in tests $I$, $II$, and $III$ are respectively $p$, $q$, and $1/2$. If the probability of the student being successful is $1/2$, then:

Let $A$ and $B$ be events in a sample space $S$ such that $P(A)=0.5$, $P(B)=0.4$ and $P(A \cup B)=0.6$. Observe the following lists. Match List-$I$ with List-$II$ and select the correct option.

List-$I$	List-$II$
$(i) \ P(A \cap B)$	$(1) \ 0.4$
$(ii) \ P(A \cap \bar{B})$	$(2) \ 0.2$
$(iii) \ P(\bar{A} \cap B)$	$(3) \ 0.3$
$(iv) \ P(\bar{A} \cap \bar{B})$	$(4) \ 0.1$

An experiment consists of recording the boy-girl composition of families with $2$ children. What is the sample space if we are interested in the number of girls in the family?

Let $A$ and $B$ be two events such that $P(\overline{A \cup B}) = \frac{1}{6}$,$P(A \cap B) = \frac{1}{4}$ and $P(\bar{A}) = \frac{1}{4}$,where $\bar{A}$ stands for the complement of the event $A$. Then the events $A$ and $B$ are