Question

A question of mathematics was given to solve three students through whom the probability of solving is $\frac{1}{2},\frac{1}{3},\frac{1}{4}$ respectively, if they all try to solve, then find the probability of solving the question?

Answer 1

$P\left(A\right)=\frac{1}{2}$

$P\left(B\right)=\frac{1}{3}$

$P\left(C\right)=\frac{1}{4}$

$\therefore$ Probability that the problem is not solved

$=(1-\frac{1}{2})(1-\frac{1}{3})(1-\frac{1}{4})$

$=\left(\frac{1}{2}\right)\left(\frac{3-1}{3}\right)\left(\frac{4-1}{4}\right)$

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

Hence, the probability that the problem is solved is $1-\frac{1}{4}=\frac{4-1}{4}=\frac{3}{4}$.