Four coins are tossed. The probability that at least one head turns up is:

$4$-digit numbers are formed using the digits $4, 5, 6, 7, 8, 9$ allowing repetition of the given digits. If a number is chosen at random from those numbers thus formed, then the probability that it is exactly divisible by $3$ is

An event $A$ is independent of itself if $P(A) = \dots$

Describe the sample space for the indicated experiment: $A$ coin is tossed and then a die is rolled only in case a head is shown on the coin.

The probabilities of a student getting $I, II$ and $III$ division in an examination are respectively $\frac{1}{10}, \frac{3}{5}$ and $\frac{1}{4}$. The probability that the student fails in the examination is

$A$ card is selected from a pack of $52$ cards. How many points are there in the sample space?