Question

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

Answer 1

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

$=P(\overline{A}\cap \overline{B}\cap \overline{C})$

$=P\left(\overline{A}\right)P\left(\overline{B}\right)P\left(\overline{C}\right)$

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

problem solved = $1-\frac{1}{4}=\frac{3}{4}$