It is given that the events A and B are such that P ( A ) = 4 1 , P ( A ∣ B ) = 2 1 and P ( B ∣ A ) = 3 2 . Then P ( B ) is

P ( A ) = 1/4 , P ( A / B ) = 2 1 , P ( B / A ) = 2/3 By conditional probability, P ( A ∩ B ) = P ( A ) P ( B / A ) = P ( B ) P ( A / B ) ⇒ 4 1 × 3 2 = P ( B ) × 2 1 ⇒ P ( B ) = 3 1

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MathematicsProbabilityGeometrical ProbabilityEasy2 minPYQ_2009

MathematicsEasysingle choice

It is given that the events $A$ and $B$ are such that $P (A) = \frac{1}{4}, P (A ∣ B) = \frac{1}{2}$ and $P (B ∣ A) = \frac{2}{3}$ . Then $P (B)$ is

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Solution:

$P (A) = 1/4, P (A / B) = \frac{1}{2}, P (B / A) = 2/3$ By conditional probability, $P (A \cap B) = P (A) P (B / A) = P (B) P (A / B) \Rightarrow \frac{1}{4} \times \frac{2}{3} = P (B) \times \frac{1}{2} \Rightarrow P (B) = \frac{1}{3}$

Stream:BITSATSubject:MathematicsTopic:ProbabilitySubtopic:Geometrical Probability

⏱ 2mℹ️ Source: PYQ_2009

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