Consider the experiment of rolling a die. Let $A$ be the event 'getting a prime number ', $B$ be the event 'getting an odd number '. Write the sets representing the events $A$ but not $B$

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

Two dice are thrown. The events $A,\, B$ and $C$ are as follows:

$A:$ getting an even number on the first die.

$B:$ getting an odd number on the first die.

$C:$ getting the sum of the numbers on the dice $\leq 5$

State true or false $:$ (give reason for your answer)

Statement :  $A^{\prime}$, $B^{\prime}, C$ are mutually exclusive and exhaustive.

Two card are drawn successively with replacement from a pack of $52$ cards. The probability of drawing two aces is

Consider the experiment of rolling a die. Let $A$ be the event 'getting a prime number ', $B$ be the event 'getting an odd number '. Write the sets representing the events $A$ and $B$

If $A$ and $B$ are two independent events such that $P\,(A \cap B') = \frac{3}{{25}}$ and $P\,(A' \cap B) = \frac{8}{{25}},$ then $P(A) = $