Let A and E be any two events with positive probabilities Statement I: P E / A ≥ P A / E P E .…

Let A and E be any two events with positive probabilities 

Statement I: PE/A≥PA/EPE.

Statement II: PA/E≥PA∩E.
  1. Both the statements are false
  2. Both the statements are true
  3. Statement - I is false, Statement - II is true
  4. Statement - I is true, Statement - II is false

Solution

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.

Asked in: JEE Main 2014 (19 Apr Online)

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