The chance of getting a doublet with $2$ dice is

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

$A$ bag contains $6$ white,$5$ black,and $4$ red balls. Find the probability of getting a white or a black ball when one ball is drawn from the bag.

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

In an experiment of throwing three fair dice,the probability of getting a sum of $16$ is ..........

If a point $A(x, y)$ lies in the region bounded by the $y$-axis,straight lines $2y+x=6$ and $5x-6y=30$,then the probability that $y < 1$ is