The probability that in a year of the $22^{nd}$ century chosen at random there will be $53$ Sundays is

$A$ bag $X$ contains $2$ white and $3$ black balls and another bag $Y$ contains $4$ white and $2$ black balls. One bag is selected at random and a ball is drawn from it. Then the probability for the ball chosen to be white 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?

$A$ man and a woman appear in an interview for two vacancies in the same post. The probability of the man's selection is $1/4$ and that of the woman's selection is $1/3$. What is the probability that none of them will be selected?

An urn contains $6$ blue, $4$ red, $3$ green, and $2$ yellow marbles. If four marbles are picked at random, what is the probability that at least one is red?

In a single throw of $2$ dice,find the probability of getting a total of $3$ or $5$.