For two events $A$ and $B,$ if $P\left( A \right) = P\left( {\frac{A}{B}} \right) = \frac{1}{4}\;\,{\rm{and}}\,\,P\left( {\frac{B}{A}} \right) = \frac{1}{2},$ then

$P\left( {\frac{{A'}}{B}} \right) = \frac{3}{4}$

JEE MATHEMATICS MCQ: PROBABILITY

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For two events

A

and

B,

P\left( A \right) = P\left( {\frac{A}{B}} \right) = \frac{1}{4}\;\,\mathrm{and}\,\,P\left( {\frac{B}{A}} \right) = \frac{1}{2},

then

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Correct option: C

P\left( {\frac{{B'}}{{A'}}} \right) = \frac{1}{2}

Option D (

P(\frac{{B'}}{{A'}}) = \frac{1}{2}

) is correct because after calculating the probabilities of the intersections and conditional probabilities, it satisfies the given conditions and independence.

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