The probability of happening an event $A$ in one trial is $0.4$. The probability that the event $A$ happens at least once in three independent trials is

From a pack of $52$ cards one card is drawn at random, the probability that it is either a king or a queen is

A die is thrown. Describe the following events : $A$ : a number less than $7.$ , $B:$ a number greater than $7.$ Find the $A \cap B$

Two cards are drawn one by one at random from a pack of $52$ cards. The probability that both of them are king, is

Suppose $3$ bulbs are selected at random from a lot. Each bulb is tested and classified as defective $(D)$ or non-defective $(N)$. Write the sample space of this experiment?

Let $\mathrm{X}$ and $\mathrm{Y}$ be two events such that $\mathrm{P}(\mathrm{X})=\frac{1}{3}, \mathrm{P}(\mathrm{X} \mid \mathrm{Y})=\frac{1}{2}$ and $\mathrm{P}(\mathrm{Y} \mid \mathrm{X})=\frac{2}{5}$. Then

$[A]$ $\mathrm{P}\left(\mathrm{X}^{\prime} \mid \mathrm{Y}\right)=\frac{1}{2}$   $[B]$ $\mathrm{P}(\mathrm{X} \cap \mathrm{Y})=\frac{1}{5}$    $[C]$ $\mathrm{P}(\mathrm{X} \cup \mathrm{Y})=\frac{2}{5}$    $[D]$ $\mathrm{P}(\mathrm{Y})=\frac{4}{15}$