A problem in statistics is given to three students $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$. Their chances…
A problem in statistics is given to three students $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$. Their chances of solving
the problem are $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ respectively. If all of them try independently, then the
probability that the problem is solved, is
$\frac{2}{3}$
$\frac{1}{2}$
$\frac{3}{4}$
$\frac{1}{4}$
Solution
P (Problem will be solved)
$=1-\mathrm{P}$ (Problem will not be solved by $\mathrm{P}, \mathrm{Q} \& \mathrm{R}$ )
$=1-\left[\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\right]$ $=1-\left(\frac{1}{2} \times \frac{2}{3} \times \frac{3}{4}\right)=1-\frac{1}{4}=\frac{3}{4}$