JEE Main 2022 · 25 Jun · Shift 1 · Mathematics Q10

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MathematicsSingle correct+4 / -1Question 10 of 90

Let $E_1$ and $E_2$ be two events such that the conditional probabilities $P(E_1|E_2)=\dfrac12$ , $P(E_2|E_1)=\dfrac34$ and $P(E_1\cap E_2)=\dfrac18$ . Then :

P(E_1\cap E_2)=P(E_1)\cdot P(E_2)

P(E_1'\cap E_2')=P(E_1')\cdot P(E_2)

P(E_1\cap E_2')=P(E_1)\cdot P(E_2)

P(E_1'\cap E_2)=P(E_1)\cdot P(E_2)

Answer and worked solution

Official answer: C

Marginals. $P(E_2)=\dfrac{1/8}{1/2}=\dfrac14$ , $P(E_1)=\dfrac{1/8}{3/4}=\dfrac16$ , so $P(E_1)P(E_2)=\dfrac1{24}$ .

Check (C). $P(E_1\cap E_2')=\dfrac16-\dfrac18=\dfrac1{24}$ . ✓

(A) fails since $\frac18\ne\frac1{24}$ ; (B) and (D) fail similarly.

(C)

Topics:Conditional probability Independent events

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JEE Main 2022 · 25 Jun · Shift 1, Mathematics question 10