JEE Main 2014 · 6 Apr · Shift 1 · Mathematics Q86

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MathematicsSingle correct+4 / -1Question 86 of 90

Let A and B be two events such that $P\left(\overline{A\cup B}\right)=\dfrac16$ , $P(A\cap B)=\dfrac14$ and $P\left(\bar A\right)=\dfrac14$ , where $\bar A$ stands for the complement of the event A. Then the events A and B are :

independent but not equally likely.

independent and equally likely.

mutually exclusive and independent.

equally likely but not independent.

Answer and worked solution

Official answer: A

$P(A\cup B)=\frac56$ and $P(A)=\frac34$ , so $P(B)=\frac56-\frac34+\frac14=\frac13$ .

$P(A)P(B)=\frac14=P(A\cap B)$ , so the events are independent. $P(A)\ne P(B)$ , so they are not equally likely.

Topics:Independent events Classical probability

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JEE Main 2014 · 6 Apr · Shift 1, Mathematics question 86