# A problem is given to three students whose probabilities of solving it are and   respectively. If the events of solving the problem are independent, find the probability that at least one of them solves it.

$E_{1}: Student 1 is able to solve the problem$

$P(E_{1}) = \frac{1}{3}$

$E_{2}: Student 2 is able to solve the problem$

$P(E_{2}) = \frac{1}{4}$

$E_{3}: Student 3 is able to solve the problem$

$P(E_{3}) = \frac{1}{6}$

$\\ P(Atlest one will able to solve ) =1- P(E'_{1}) \cdot P(E'_{2}) \cdot P(E'_{3})\\\\ = 1- \frac{2}{3} \times \frac{3}{4} \times \frac{5}{6} \\\\= \frac{72-30}{72} \\\\ = \frac{7}{12}$

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