From the word $POSSESSIVE$,a letter is chosen at random. The probability of it being $S$ is

Let $A$ be the event that the absolute difference between two randomly chosen real numbers in the sample space $[0, 60]$ is less than or equal to $a$. If $P(A) = \frac{11}{36}$,then $a$ is equal to $...............$.

$A$ coin is tossed $3$ times. The probability of obtaining at least two heads is

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

If $\frac{1+3P}{3}$ and $\frac{1-2P}{2}$ are probabilities of two mutually exclusive events,then $P$ lies in the interval.

If $A$,$B$,and $C$ are mutually exclusive and exhaustive events of a sample space $S$ such that $P(B) = \frac{3}{2} P(A)$ and $P(C) = \frac{1}{2} P(B)$,then $P(A) = $