Important Formulas on Probability

Probability of an Event:

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

Addition Rule:

For any two events A and B,

P(A ⋃ B) = P(A) + P(B) – P(A ⋂ B)

If A and B are mutually exclusive (disjoint),   

P(A ⋃ B) = P(A) + P(B)

Multiplication Rule:

For any two events A and B,

P(A ⋂ B) = P(A) · P(B | A)

If A and B are independent,

P(A ⋂ B) = P(A) · P(B)

Conditional Probability:

P(B | A) = P(A ⋂ B) / P(A)

Bayes’ Theorem:

P(A | B) = [P(B | A) · P(A)] / P(B)

Total Probability Rule:

If B1, B2, …, Bn are mutually exclusive and exhaustive events,

P(A) = P(A ⋂ B1) + P(A ⋂ B2) + … + P(A ⋂ Bn)

Probability is an important chapter for the students of Class 9, 10, 11, and 12. The Probability Questions, with their answers included in this article, will help you understand the basic concepts and formula. These questions cover concepts like Sample Space, Events, Coin Probability, etc. Solving these problems will improve your understanding and problem-solving skills in probability.