The probability of getting head and tail alternately in three throws of a coin (or a throw of three coins) is:

$A$ determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that the determinant chosen is non-zero is

Two numbers $a$ and $b$ are chosen at random from the set of first $30$ natural numbers. The probability that $a^2 - b^2$ is divisible by $3$ is

The probability that a leap year selected at random contains either $53$ Sundays or $53$ Mondays is

$2$ dice are thrown. Find the probability of getting an odd number on $1$ die and a multiple of $3$ on the other.

There are $5$ volumes of Mathematics among $25$ books. They are arranged on a shelf in random order. The probability that the volumes of Mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is