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Events can be classified based on the possibility of their occurrences.

1. Equally likely event: If the probability of two or more events happening is the same, then it is an equally likely event.
Example:
Let us consider the event of tossing a coin.

The sample space, $$S = \{H, T\}$$

The probability of getting a head, $$P(H) = \frac{1}{2}$$

The probability of getting a tail, $$P(T) = \frac{1}{2}$$

$$P(H) = P(T) = \frac{1}{2}$$

Thus, the events $$P(H)$$ and $$P(T)$$ are equally likely events.

2. Sure or certain event: A certain event will have a probability of $$1$$.
Example:
On rolling a die, the probability of getting a number lesser than $$7$$ is a sure event.

3. Impossible event: An impossible event will have a probability of $$0$$.
Example:
On rolling a die, the probability of getting a number greater than $$7$$ is an impossible event.

4. Mutually exclusive events: Two events that cannot occur at the same time are called mutually exclusive events.
Example:
While tossing a fair coin, we can either get heads or tails.

5. Complementary events: For an event $$E$$, let the outcome obtained for the event be $$A$$. Also, let the outcome not accepted for the event be $$A'$$. In this case, the complementary event to $$A$$ is $$A'$$.

If $$S$$ is the sample space and $$A$$ is the set of favourable outcomes of that event, then the complimentary event $$A$$' is $$S - A$$.
Example:
Consider the event of rolling a fair die.

The sample space, $$S = \{1, 2, 3, 4, 5, 6\}$$

The outcome of the event $$A$$ is $$\{1, 2, 3\}$$.

Therefore, the outcome of its complementary event $$A'$$ $$= S - A$$

$$= \{1, 2, 3, 4, 5, 6\} - \{1, 2, 3\}$$

$$=$$ $$\{4, 5, 6\}$$.