01 · DEFINITION
Classical / Theoretical Probability
The theoretical probability P(E) of an event E occurring in a random experiment with equally likely outcomes is defined as:
P(E) = (Number of outcomes favorable to E) / (Total number of possible outcomes)
Probability Range Limit
The probability of any event E is always a number between 0 and 1 inclusive:
0 ≤ P(E) ≤ 1
02 · EVENT TYPES
Classification of Events
Impossible Event
Impossible Event
An event that has 0 favorable outcomes. P(E) = 0 (e.g., getting a 7 on a standard 6-sided die).Sure / Certain Event
Sure or Certain Event
An event that is 100% guaranteed to happen. P(E) = 1 (e.g., getting a number less than 7 on a die).Elementary Event
Elementary Event
An event having only one outcome. The sum of probabilities of all elementary events of an experiment equals 1.Complementary Events
Complementary Events (E and Ē)
Event Ē represents "NOT E". P(E) + P(Ē) = 1 ⟹ P(Ē) = 1 - P(E).03 · SOLVED NCERT EXAMPLE
Step-by-Step Problem Solving
EXAMPLE 1
If P(E) = 0.05, what is the probability of 'not E'?
By the complementary event rule P(E) + P(NOT E) = 1:
P(NOT E) = 1 - P(E)
P(NOT E) = 1 - 0.05 = 0.95
P(NOT E) = 1 - 0.05 = 0.95
04 · QUICK SUMMARY
Key Takeaways
01
P(E) = Favorable Outcomes / Total Outcomes.
02
Probability ranges from 0 (impossible) to 1 (certain).
03
Complementary rule: P(NOT E) = 1 - P(E).