JEE Main 2022 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 25 June 2022, Shift 1, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

Let

E_1

and

E_2

be two events such that the conditional probabilities

P(E_1|E_2)=\frac{1}{2}

P(E_2|E_1)=\frac{3}{4}

and

P(E_1\cap E_2)=\frac{1}{8}

. Then :

(1) $P(E_1\cap E_2)=P(E_1)\cdot P(E_2)$
(2) $P(E_1'\cap E_2')=P(E_1')\cdot P(E_2)$
(3) $P(E_1\cap E_2')=P(E_1)\cdot P(E_2)$ Official answer
(4) $P(E_1'\cap E_2)=P(E_1)\cdot P(E_2)$

Official answer

Option 3

NTA final key.

Chapter: Probability
Topic: Conditional Probability
Idea tested: Independence Criterion

Same idea in other shifts

Asked 5× in all

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.