If P ( A ∪ B ) = 3 2 , P ( A ∩ B ) = 6 1 and P ( A ) = 3 1 then

P ( A ∪ B ) = P ( A ) + P ( B ) − P ( AB ) ⇒ 3 2 = 3 1 + P ( B ) − 6 1 ⇒ P ( B ) = 2 1 Now, P ( AB ) = P ( A ) P ( B ) , A and B are independent events.

Mathematics - Probability Question with Solution | TestHub

MathematicsProbabilityGeneral (Event SS, Definitions, Odd against/Favour)Medium2 minPYQ_2010

MathematicsMediumsingle choice

If $P (A \cup B) = \frac{2}{3}, P (A \cap B) = \frac{1}{6}$ and $P (A) = \frac{1}{3}$ then

Options:

Answer:

Solution:

$P (A \cup B) = P (A) + P (B) - P (AB)$ $\Rightarrow \frac{2}{3} = \frac{1}{3} + P (B) - \frac{1}{6} \Rightarrow P (B) = \frac{1}{2}$ Now, $P (AB) = P (A) P (B), A$ and $B$ are independent events.

Stream:BITSATSubject:MathematicsTopic:ProbabilitySubtopic:General (Event SS, Definitions, Odd against/Favour)

⏱ 2mℹ️ Source: PYQ_2010

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