JEE Main 2014MathematicsProbabilityMediumMCQ

JEE Main 2014 — Probability Question with Solution

JEE Main 2014 (19 Apr Online)

Question

Let A and E be any two events with positive probabilities 

Statement I: PE/A≥PA/EPE.

Statement II: PA/E≥PA∩E.

Choose an option

Show full solutionCorrect option: B
Correct answer
BBoth the statements are true

Step-by-step explanation

We know that PE/A=PE∩APA

⇒PE∩A=PE/A·PA   ...i

Also, PA/E=PE∩APE

⇒PE∩A=PA/E·PE   ii

From the equations i and ii, we get

PE/A·PA=PA/E·PE

Now, since 0<PA≤1

⇒PE/A≥PA/E·PE

Again, we have PA/E=PE∩APE

⇒PA/E·PE=PE∩A

Now, since 0<PE≤1

PA/E≥PA∩E

⇒Both the statements are true.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Probability chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

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.