$A$ die is thrown. Find the probability of the following event: $A$ number greater than or equal to $3$ will appear.

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 be a black card (i.e.,a club or a spade).

$A$ coin is tossed three times. Consider the following events:
$A$: 'No head appears',
$B$: 'Exactly one head appears',
$C$: 'At least two heads appear'.
Do they form a set of mutually exclusive and exhaustive events?

If $A$ and $B$ are two events such that $P(A) = \frac{1}{4}$,$P(B) = \frac{1}{2}$,and $P(A \cap B) = \frac{1}{8}$,find $P(\text{not } A \text{ and not } B)$.

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 random experiment of selecting a ticket from $50$ tickets numbered $00, 01, 02, 03, ..., 47, 49$,if a ticket is selected such that the product of its digits is $0$,what is the probability that the sum of its digits is $8$?