Let $S$ be the set of all quadratic equations of the form $x^2+bx+c=0$,where $b, c \in \{1, 2, 3, 4, 5, 6\}$. If an equation is selected at random from $S$,then the probability that the equation has real roots is

If $A$ and $B$ are events such that $P(A \cup B) = 3/4,$ $P(A \cap B) = 1/4,$ and $P(\bar{A}) = 2/3,$ then $P(\bar{A} \cap B)$ is

Three coins are tossed once. Find the probability of getting exactly $2$ tails.

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

Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}$. Then the probability that the problem is solved correctly by at least one of them is

Two dice are thrown independently. Let $A$ be the event that the number appeared on the $1^{\text{st}}$ die is less than the number appeared on the $2^{\text{nd}}$ die,$B$ be the event that the number appeared on the $1^{\text{st}}$ die is even and that on the $2^{\text{nd}}$ die is odd,and $C$ be the event that the number appeared on the $1^{\text{st}}$ die is odd and that on the $2^{\text{nd}}$ die is even. Then