JEE Main 2014 · 19 Apr · Shift 1 · Mathematics Q86

MathematicsSingle correct+4 / -1Question 86 of 90

Let A and E be any two events with positive probabilities :

Statement - 1 : $P(E/A)\ge P(A/E)P(E)$

Statement - 2 : $P(A/E)\ge P(A\cap E)$ .

Both the statements are true

Both the statements are false

Statement - 1 is true, Statement - 2 is false

Statement - 1 is false, Statement - 2 is true.

Answer and worked solution

Official answer: A

Statement 1: $P(A/E)P(E)=P(A\cap E)$ and $P(E/A)=\dfrac{P(A\cap E)}{P(A)}\ge P(A\cap E)$ . True.
Statement 2: $P(A/E)=\dfrac{P(A\cap E)}{P(E)}\ge P(A\cap E)$ . True.

Both are true.

JEE Main 2014 · 19 Apr · Shift 1, Mathematics question 86