$A$ coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows $6$ is

$A$ box contains $1$ red and $3$ identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

In a college, $40 \%$ of students attend the Mathematics class, $30 \%$ of students attend the Physics class, and $20 \%$ of students attend both classes. If a student is chosen at random from the college, what is the probability that the chosen student attends only one class?

Three dice are thrown simultaneously. What is the probability of obtaining a total of $17$ or $18$?

If $\frac{1 + 3p}{3}, \frac{1 - p}{4}$ and $\frac{1 - 2p}{2}$ are the probabilities of three mutually exclusive events,then the set of all values of $p$ is

Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N - 2, \sqrt{3N}, N + 2$ are in geometric progression be $\frac{k}{48}$. Then the value of $k$ is