JEE Main 2014MathematicsProbabilityHardMCQ

JEE Main 2014 — Probability Question with Solution

JEE Main 2014 (06 Apr)

Question

Let A and B be two events such that PA∪B¯=16, PA∩B=14 and PA¯=14, where A¯ stands for the complement of the event A. Then the events A and B are 

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Show full solutionCorrect option: A
Correct answer
AIndependent but not equally likely.

Step-by-step explanation

PA∪B¯=16         

∴    PA∪B=56

PA∩B=14

PA¯=14         

∴    PA=34

∴    PA∪B=PA+PB-PA∩B

∴    56=34+PB-14

∴    PB=13

∴    PA·PB=13×34=14=PA∩B

Therefore, A and B are independent and since PA≠PB they are not equally likely.

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About this question

This is a previous-year question from JEE Main 2014, 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.