If A, B, C are mutually exclusive and exhaustive events associated to

1.	If A, B, C are mutually exclusive and exhaustive events associated to a random experiment, then write the value of P(A) + P(B) + P(C).
Answer» Given P(A ∩ B) = P(B ∩ C) = P(A ∩ C) = 0 ⇒ P(A ∩ B ∩ C) = 0 Also given P(A ∪ B ∪ C) = 1 By formula we know, P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(A ∩ B ∩ C) Substituting the values we get 1 = P(A) + P(B) + P(C) ⇒ P(A) + P(B) + P(C) = 1

If A, B, C are mutually exclusive and exhaustive events associated to a random experiment, then write the value of P(A) + P(B) + P(C).

Answer»

Given

P(A ∩ B) = P(B ∩ C) = P(A ∩ C) = 0

⇒ P(A ∩ B ∩ C) = 0

Also given P(A ∪ B ∪ C) = 1

By formula we know,

P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(A ∩ B ∩ C)

Substituting the values we get

1 = P(A) + P(B) + P(C)

⇒ P(A) + P(B) + P(C) = 1

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If A, B, C are mutually exclusive and exhaustive events associated to a random experiment, then write the value of P(A) + P(B) + P(C).

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