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.

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