Some Relations Between Independence and Mutually Exclusiveness of Two Events
Probability of Class 12
(i) If two events A ≠ Φ and B ≠ Φ are independent, then they are not mutually exclusive.
(ii) If two events A ≠ Φ and B ≠ Φ are mutually exclusive, then they are not independent.
(iii) If three events A ≠ Φ, B ≠ Φ and C ≠ Φ are independent, then they are not mutually exclusive. Rather none of the pairs A, B; B, C and C, A is mutually exclusive.
(iv) If three events A ≠ Φ, B ≠ Φ and C ≠ Φ are such that any two of these are mutually exclusive then A, B and C are not independent.
e.g. Say A and B are mutually exclusive, then P(A ∩ B) = 0 and so P(A ∩ B ∩ C) ≤ P(A ∩ B) = 0
i.e. P(A ∩ B ∩ C) = 0 but P(A).P(B).P(C) ≠ 0.
∴ A, B and C are not independent.
- Important Terminology
- Algebra of Events
- Probability of an Event
- Conditional Probability
- Independent Events
- Some Relations Between Independence and Mutually Exclusiveness of Two Events
- Binomial Distribution for Successive Events
- Bayes Theorem
- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
