Chapter 14: Probability

Refined and Comprehensive Class 10 Mathematics Notes

Core Concepts & Formulas

1. Classical Definition of Probability

The probability of an event E, denoted as P(E), is given by:

P(E) = Number of favorable outcomes / Total number of equally likely outcomes

2. Key Probability Properties

0 ≤ P(E) ≤ 1
P(E) + P(not E) = 1 ⇒ P(not E) = 1 - P(E)

Points to Remember

Extreme Probabilities: The probability of an impossible event is 0, while the probability of a sure or certain event is 1.
Complementary Events: The event 'not E' is called the complement of event E. The sum of probabilities of all elementary events of an experiment is always equal to 1.

Important Practice Questions

  1. Find the probability of getting a particular number or condition when a die is thrown once or twice.
  2. Find the probability involving cards drawn from a standard deck of 52 playing cards.
  3. Find the probability of complementary events using the relationship P(not E) = 1 - P(E).

Quick Revision

Classical Probability

P(E) = Favorable Outcomes / Total Outcomes

Probability Range

0 ≤ P(E) ≤ 1 (Never negative or > 1)

Complementary Rule

P(not E) = 1 - P(E)

Special Events

Impossible Event = 0 | Certain Event = 1