NIMCET 2015 — Mathematics PYQ

Maximum Value:

$P(A\cap B)\le \min (P(A),P(B))$

$P(A\cap B)\le \min (\frac{1}{2},\frac{1}{3})$

$P(A\cap B)\le \frac{1}{3}$

Minimum Value (Standard Reference):

For independent events:

$P(A\cap B)=P(A)\cdot P(B)$

$P(A\cap B)=\frac{1}{2}\cdot \frac{1}{3}=\frac{1}{6}$

Range:

$\frac{1}{6}\le P(A\cap B)\le \frac{1}{3}$

Correct Option: (c)