Probability | Class 11 Mathematics Notes

14.1.2 Types of events

This subsection classifies events into different types based on the elements they contain. The primary types discussed are:

1. Impossible and Sure Events: The empty set φ represents an impossible event, which cannot occur under any outcome. For example, in rolling a die, the event 'number is a multiple of 7' corresponds to φ since no die face shows a multiple of 7. The entire sample space S represents a sure event, which always occurs, such as 'number is odd or even' when rolling a die.

2. Simple (Elementary) Event: An event containing exactly one sample point. For a sample space with n distinct elements, there are exactly n simple events. For example, tossing two coins, the simple events are {HH}, {HT}, {TH}, and {TT}.

3. Compound Event: An event containing more than one sample point. For example, tossing three coins, the event 'exactly one head appears' corresponds to the subset {HTT, THT, TTH}, which has multiple outcomes.

Understanding these types helps in analyzing events and their probabilities effectively.

🧪 Activity: Identify simple and compound events in tossing two or three coins and classify events as impossible or sure in rolling a die.

🔗 Connection: This section prepares the understanding of operations on events, which is discussed next under algebra of events.