JEE Main 2017MathematicsProbabilityMediumMCQ

JEE Main 2017 — Probability Question with Solution

JEE Main 2017 (09 Apr Online)

Question

Let E & F be two independent events. The probability that E & F happen is 112 and the probability that neither E nor F happens is 12 , then a value of PEPF is:

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Show full solutionCorrect option: A
Correct answer
A43

Step-by-step explanation

PE∩F=PE. PF=112

⇒xy=112

⇒PE-∩F-=PE- . PF-=12

⇒ 1-PE 1-PF=12

⇒1-x-y+xy=12

⇒1-x-y+112=12

⇒1-x-y=12-112=512

⇒x+y=712

⇒x+112x=712

⇒⇒12x2+112x=712

⇒12x2-7x+1=0

⇒12x2-4x-3x+1=0

⇒4x3x-1-13x-1=0

⇒x=13, x=14

⇒y=14, y=13

⇒xy=1314 & 1413

⇒xy=43 & 34

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About this question

This is a previous-year question from JEE Main 2017, covering the Probability chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.