One card is drawn from a well-shuffled deck of $52$ cards. If each outcome is equally likely,calculate the probability that the card will not be a diamond.

Two dice are thrown independently. Let $A$ be the event that the number appeared on the $1^{\text{st}}$ die is less than the number appeared on the $2^{\text{nd}}$ die,$B$ be the event that the number appeared on the $1^{\text{st}}$ die is even and that on the $2^{\text{nd}}$ die is odd,and $C$ be the event that the number appeared on the $1^{\text{st}}$ die is odd and that on the $2^{\text{nd}}$ die is even. Then

In each of the following experiments,specify the appropriate sample space: $A$ boy has a $1$ rupee coin,a $2$ rupee coin,and a $5$ rupee coin in his pocket. He takes out two coins out of his pocket,one after the other.

$A$ box contains $6$ red marbles numbered from $1$ through $6$ and $4$ white marbles numbered $12$ through $15$. Find the probability that a marble drawn at random is white and odd-numbered.

Which of the following cannot be a valid assignment of probabilities for outcomes of sample space $S = \{\omega_{1}, \omega_{2}, \omega_{3}, \omega_{4}, \omega_{5}, \omega_{6}, \omega_{7}\}$?

Outcome	Probability
$\omega_{1}$	$\frac{1}{14}$
$\omega_{2}$	$\frac{2}{14}$
$\omega_{3}$	$\frac{3}{14}$
$\omega_{4}$	$\frac{4}{14}$
$\omega_{5}$	$\frac{5}{14}$
$\omega_{6}$	$\frac{6}{14}$
$\omega_{7}$	$\frac{15}{14}$

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.