What is the probability of getting at least one tail when a coin is tossed $4$ times?

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

Two students appeared simultaneously for an entrance exam. If the probability that the first student gets qualified in the exam is $\frac{1}{4}$ and the probability that the second student gets qualified in the same exam is $\frac{2}{5}$,then the probability that at least one of them gets qualified in that exam is

If $X_1, X_2, \ldots, X_n$ are $n$ independent events such that $P(X_r) = \frac{1}{r+1}$ for $r = 1, 2, \ldots, n$,then the probability that none of the $n$ events occur is

$A$ coin is tossed and a die is thrown. The probability that the outcome will be a head or a number greater than $4$ or both,is

$A$ coin is tossed again and again. If tail appears on the first three tosses, then the chance that head appears on the fourth toss is