Question

A problem in calculus is given to two students $A$ and $B$, whose chances of solving it are $\frac{1}{3}$ and $\frac{1}{4}$ respectively. Find the probability of the problem being solved, if both of them try independently.

Answer 1

Here $P\left(A\right)=\frac{1}{3}$ and $P\left(B\right)=\frac{1}{4}$

The probability that the problem is solved will be found by finding the probability that either $A$ solves or $B$ solves or both $A$ and $B$ solve the problem.

Probability of problem being solved $=P\left(A\right)P\left(\overline{B}\right)+P\left(\overline{A}\right)P\left(B\right)+P\left(A\right)P\left(B\right)$

$=\frac{1}{3}\cdot \frac{3}{4}+\frac{2}{3}\cdot \frac{1}{4}+\frac{1}{3}\cdot \frac{1}{4}=\frac{6}{12}=\frac{1}{2}$