If A ,B ,C are three mutually exclusive and exhaustive events of an experiment such that P (A )=2P (B )=3P (C ), then P (B ) is equal to

Question

Accepted Answer

Correct answer: B. (b) : We have, A ,B ,C are mutually exclusive and exhaustive events. ∴ A ∩B=B ∩C=C ∩A=A ∩B ∩C= ⇒ P (A ∩B )=P (B ∩C )=P (C ∩A )=P (A ∩B ∩C )=0 Now, P (A )=2P (B )=3P (C ) ⇒ P (A )=2P (B ) and P (C )= 23P (B ) ∴ P (A ∪B ∪C )=P (A )+P (B )+P (C ) ⇒ 1=2P (B )+P (B )+ 23P (B ) ⇒1= 113P (B ) ⇒P (B )= 311

$If A, B, C are three mutually exclusive and exhaustive events of an experiment such that P (A) = 2 P (B) = 3 P (C), then P (B) is equal to$

Solution

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