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

In an experiment of tossing a coin and a fair die,the probability of getting a head on the coin and $6$ on the die 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

$A$ letter is chosen at random from the word $ASSASSINATION$. Find the probability that the letter is a vowel. (in $/13$)

Let $A$, $B$, and $C$ be three events such that $P(A \cap \bar{B} \cap \bar{C}) = 0.6$, $P(A) = 0.8$, and $P(\bar{A} \cap B \cap C) = 0.1$. Then, the value of $P(\text{at least two among } A, B, \text{ and } C)$ equals:

In a competition,$A, B$,and $C$ are participating. The probability that $A$ wins is twice that of $B$,and the probability that $B$ wins is twice that of $C$. Then,the probability that $A$ loses is: