$A$ card is selected from a pack of $52$ cards. Calculate the probability that the card is a black card.

$A$ six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be $7$. The probability that the number $3$ has appeared at least once 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 $\leq 5$.
Describe the events $B$ and $C$.

In a lottery containing $35$ tickets,exactly $10$ tickets bear a prize. If a ticket is drawn at random,then the probability of not getting a prize is

The probability of hitting a target by three marksmen is $\frac{1}{2}, \frac{1}{3},$ and $\frac{1}{4}$ respectively. If the probability that exactly two of them will hit the target is $\lambda$ and that at least two of them hit the target is $\mu,$ then $\lambda + \mu$ is equal to :-

$A$ die is thrown. Find the probability of the following event: $A$ prime number will appear.