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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 \(A'\) \(= S - A\)
\(= \{1, 2, 3, 4, 5, 6\} - \{1, 2, 3\}\)
\(=\) \(\{4, 5, 6\}\).
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