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

If two dice are thrown,then the probability of getting coprime numbers on the dice is

Consider the experiment in which a coin is tossed repeatedly until a head comes up. Describe the sample space.

The probability of choosing randomly a number $c$ from the set $\{1, 2, 3, \ldots, 9\}$ such that the quadratic equation $x^2 + 4x + c = 0$ has real roots is

$A$ problem in mathematics is given to $4$ students whose chances of solving it individually are $\frac{1}{2}, \frac{1}{3}, \frac{1}{4},$ and $\frac{1}{5}.$ The probability that the problem will be solved by at least one student is

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is: