$A$ dice is rolled three times. The probability of getting a larger number than the previous number each time is:

In a class of $25$ students with roll numbers $1$ to $25,$ a student is picked up at random to answer a question. Find the probability that the roll number of the selected student is either a multiple of $5$ or $7$.

Find the probability that a two-digit number formed by the digits $1, 2, 3, 4, 5$ is divisible by $4$ (repetition of digits is allowed).

In order to get at least one head with a probability $\ge 0.9$,the minimum number of times a coin needs to be tossed is:

$A$ husband and wife appear in an interview for $2$ vacancies in the same post. The probability of husband's selection is $\frac{1}{7}$ and that of wife's is $\frac{1}{5}$. What is the probability that none of them will be selected?

$A$ pair of dice is thrown. If $5$ appears on at least one of the dice,then the probability that the sum is $10$ or greater is: