Two dice are thrown together. If the numbers appearing on the two dice are different,then what is the probability that the sum is $6$?

Let $A$ and $B$ be two independent events of a random experiment. If the probability that both $A$ and $B$ occur is $\frac{1}{6}$ and the probability that neither of them occur is $\frac{1}{3}$,then the probability of occurrence of $A$ 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. The correct match of List $I$ from List $II$ is:

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

$A$ card is drawn at random from a pack of $52$ cards. What is the probability that the drawn card is neither a heart nor a king?

$A$ and $B$ toss a coin alternatively,the first to show a head being the winner. If $A$ starts the game,the chance of his winning is

Events $E$ and $F$ are such that $P(\text{not } E \text{ and not } F) = 0.25$. State whether $E$ and $F$ are mutually exclusive.