Q. A problem in mathematics is given to three students $E_{1},\ E_{2}$ and $E_{3}$ and their respective probability of solving the problem is $\frac{1}{2},\frac{1}{3}and\frac{1}{4}$. Probability that the problem is solved is
A) 3/4
B) 1/2
C) 2/3
D) 1/3
Explanation
(a)
Given, $P\left( E_{1} \right) = \frac{1}{2},P\left( E_{2} \right) = \frac{1}{3}\ and\ P\left( E_{3} \right) = \frac{1}{4}$
$\therefore\ P\left( E_{1} \cup E_{2} \cup E_{3} \right) = 1 - P\left( {\overline{E}}_{1} \right)P\left( {\overline{E}}_{2} \right)P({\overline{E}}_{3})$
$= 1 - \left( 1 - \frac{1}{2} \right)\left( 1 - \frac{1}{3} \right)\left( 1 - \frac{1}{4} \right)$
$= 1 - \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} = \frac{3}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.