If $P(A \cup B)=0.8$ and $P(A \cap B)=0.3$, then $P(\bar{A})+P(\bar{B})$ is equal to:

Statement-$I$: If a leap year is selected at random,the probability of it having $53$ Sundays is $2/7$.
Statement-$II$: $A$ leap year has $366$ days.

Let $A$ and $B$ be two events in a random experiment. If $P(A \cap \overline{B}) = 0.1$, $P(\overline{A} \cap B) = 0.2$ and $P(B) = 0.5$, then $P(\overline{A} \cap \overline{B}) = $

The probability that a man and his wife will be alive after $20 \text{ years}$ are $\frac{1}{4}$ and $\frac{1}{3}$ respectively. The probability that neither the man nor his wife will be alive after $20 \text{ years}$ is

When a certain biased die is rolled,a particular face occurs with probability $\frac{1}{6}-x$ and its opposite face occurs with probability $\frac{1}{6}+x$. All other faces occur with probability $\frac{1}{6}$. Note that opposite faces sum to $7$ in any die. If $0 < x < \frac{1}{6}$,and the probability of obtaining a total sum of $7$ when such a die is rolled twice is $\frac{13}{96}$,then the value of $x$ is:

Two dice are rolled. Then,the probability that the total score is a prime number is