JEE Main 2014 · 9 Apr · Shift 1 · Mathematics Q87

MathematicsSingle correct+4 / -1Question 87 of 90

If A and B are two events such that $P(A\cup B)=P(A\cap B)$ , then the incorrect statement amongst the following statements is :

A and B are equally likely

P(A\cap B')=0

P(A'\cap B)=0

P(A)+P(B)=1

Answer and worked solution

Official answer: D

$P(A\cup B)=P(A\cap B)$ forces $P(A\cap B')=P(A'\cap B)=0$ , so $P(A)=P(B)=P(A\cap B)$ . Statements (1)-(3) hold.

$P(A)+P(B)=1$ need not hold (it does only when $P(A)=\frac12$ ). So (4) is the incorrect one.

JEE Main 2014 · 9 Apr · Shift 1, Mathematics question 87