Definitions [2]
Definition: Favourable Outcomes
The outcomes satisfying a particular condition are called favourable outcomes.
Definition: Event
A set of favourable outcomes of a given sample space is an ‘event’. Event is a subset of the sample space.
- Events are denoted by capital letters A, B, C, D etc.
- The number of elements in event A is written n(A).
- Since A ⊆ S, always 0 ≤ n(A) ≤ n(S).
- Example: two coins tossed, A = getting at least one tail → A = {TT, TH, HT}, n(A) = 3.
Key Points
Key Points: Elementary Types of Events and Properties of Probability
- The sample space \[ S \] contains all possible outcomes.
- An event is a subset of the sample space.
- A simple event has one outcome; a compound event has more than one outcome.
- A certain event has probability \[ 1; \] an impossible event has probability \[ 0. \]
- The complement of \[ A \] is \[ A', \] and \[ P(A') = 1 - P(A). \]
- Mutually exclusive events cannot occur together: \[ A \cap B = \varnothing. \]
- Exhaustive events together cover the entire sample space: \[ A \cup B = S. \]
- For equally likely outcomes, \[ P(A) = \frac{n(A)}{n(S)}. \]
- For any two events, \[ P(A \cup B) = P(A) + P(B) - P(A \cap B). \]
Concepts [5]
- Concept of Probability
- Occurrence of an Event
- Elementary Types of Events and Properties of Probability
- Axiomatic Approach to Probability
- Probability of 'Not', 'And' and 'Or' Events
