JEE Main 2016 · 9 Apr · Shift 1 · Mathematics Q87

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MathematicsSingle correct+4 / -1Question 87 of 90

If A and B are any two events such that $P(A)=\frac25$ and $P(A\cap B)=\frac3{20}$ , then the conditional probability, $P(A\mid(A'\cup B'))$ , where A′ denotes the complement of A, is equal to :

\dfrac14

\dfrac5{17}

\dfrac8{17}

\dfrac{11}{20}

Answer and worked solution

Official answer: B

$A'\cup B'=(A\cap B)'$ , so $P=\dfrac{P(A)-P(A\cap B)}{1-P(A\cap B)}=\dfrac{1/4}{17/20}=\dfrac5{17}$ .

Topics:Conditional probability

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JEE Main 2016 · 9 Apr · Shift 1, Mathematics question 87