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).

The coefficients $a, b$ and $c$ of the quadratic equation $ax^{2} + bx + c = 0$ are obtained by throwing a die three times. The probability that this equation has equal roots is

There are four machines and it is known that exactly two of them are faulty. They are tested,one by one,in a random order until both the faulty machines are identified. Then the probability that only two tests are needed is

An old man forgets the last two digits of a telephone number. He dials these two digits randomly. What is the probability that he dials the correct number?

$A$ box contains $5$ blue and $4$ white chalks. If two chalks are chosen at random,what is the probability that both chalks are of the same color?

Two cards are drawn from a pack of $52$ cards. What is the probability that at least one of the cards drawn is an ace?