$A$ card is selected from a pack of $52$ cards. Calculate the probability that the card is an ace.

Six faces of an unbiased die are numbered with $2, 3, 5, 7, 11$ and $13$. If two such dice are thrown, then the probability that the sum on the uppermost faces of the dice is an odd number is

$A$ man and his wife appear for an interview for two posts. The probability of the husband's selection is $\frac{1}{7}$ and that of the wife's selection is $\frac{1}{5}$. What is the probability that only one of them will be selected?

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

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 numbers $x$ and $y$ are chosen at random from the set of integers $\{1, 2, 3, 4, \dots, 15\}$. The probability that the point $(x, y)$ lies on a line passing through $(0, 0)$ with a slope of $\frac{2}{3}$ is: