Question

A problem in mathematics is given to three students whose chances of solving it are $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$ respectively. What is the probability that problem will be solved?

Answer 1

let A,B,C be events of solving problem

$\overline{A},\overline{B},\overline{C}$ be events of not solving problem

$P\left(A\right)=\frac{1}{2}$ $P\left(B\right)=\frac{1}{3}$ $P\left(C\right)=\frac{1}{4}$ $(\because P(A)+P(\overline{A})=1)$

$\therefore P\left(\overline{A}\right)=\frac{1}{2}$ $P\left(\overline{B}\right)=\frac{2}{3}$ $P\left(\overline{C}\right)=\frac{3}{4}$

P(problem is sloved) $=1-P$ (no one solves the problem)

$=1-\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}$

$=1-\frac{1}{4}$

P (Problem will be solved) $=\frac{3}{4}$