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

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 (A) (1/11) (B) (2/11) (C) (3/11) (D) (4/11)

Tardigrade Admin · Accepted Answer

Given, P(A)=2 P(B)=3 P(C) ⇒ P ( C )=2 / 3 P ( B ) Since A , B , C are three mutually exclusive and exhaustive events ∴ P(A)+P(B)+P(C)=1 ⇒ P ( B )=3 / 11

Q. 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

$\frac{1}{11}$

$\frac{2}{11}$

$\frac{3}{11}$

$\frac{4}{11}$

Given, $P (A) = 2 P (B) = 3 P (C)$
$\Rightarrow P (C) = 2/3 P (B)$
Since $A, B, C$ are three mutually exclusive and exhaustive events
$∴ P (A) + P (B) + P (C) = 1$
$\Rightarrow P (B) = 3/11$

Q. 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

111​

112​

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114​