$A$ rational number is selected at random from the distinct rational numbers of the form $p/q$ formed with $p$ and $q$ belonging to the set $\{1, 2, 3, 4, 5, 6\}$. The probability that the rational number selected is a proper fraction 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 the roots of each of the equations $2x^2+x-1=0$, $3x^2-10x+3=0$, and $6x^2+11x-2=0$ correspond to probabilities of three events of a random experiment, then those events are

Two dice are thrown. The probability that the sum of the points on two dice will be $7$ is:

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
State true or false: (give reason for your answer)
Statement: $A', B', C$ are mutually exclusive and exhaustive.

When two dice are thrown simultaneously,what is the probability that at least one of the dice shows a number greater than $3$?