Q. If $P(B) = \frac{3}{4},\ P\left( A \cap B \cap \overline{C} \right) = \frac{1}{3}\ and\ P\left( \overline{A} \cap B \cap \overline{C} \right) = \frac{1}{3},\ then\ P(B \cap C)$ is
A) $\frac{1}{12}$
B) $\frac{1}{6}$
C) $\frac{1}{15}$
D) $\frac{1}{9}$
Explanation
(a)
From Venn diagram, we can see that
[image:16_image1.emf]
$P(B \cap C) = P(B) - P\left( A \cap B \cap \overline{C} \right) - P(\overline{A} \cap B \cap \overline{C})$
$= \frac{3}{4} - \frac{1}{3} - \frac{1}{3} = \frac{1}{12}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.