A problem in Mathematics is given to three students A, B, C and their respective probability of solving the problem are 12,13 and 14. Probability that the problem is solved, is

Consider the following events:

$E$ = Student $A$ solves the problem

$F$ = Student $B$ solves the problem

$G$ = Student $C$ solves the problem

Clearly, $E, F, G$ are independent events such that

$P (E) = \frac{1}{2}, P (F) = \frac{1}{3}$ and $P (G) = \frac{1}{4}$

Required probability $= P (E \cup F \cup G)$

Required probability = $1 - P (\bar{E}) P (\bar{F}) P (\bar{G})$

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

A problem in Mathematics is given to three students $A, B, C$ and their respective probability of solving the problem are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ . Probability that the problem is solved, is