The probability of Jide, Atu and Obu solving a given problem are \(\frac{1}{12}\), \(\frac{1}{6}\) and \(\frac{1}{8}\) respectively. Calculate the probability that only one solves the problem.
A. \(\frac{1}{576}\) B. \(\frac{55}{576}\) C. \(\frac{77}{576}\) D. \(\frac{167}{576}\)
Correct Answer: D
Explanation
\(P(Jide) = \frac{1}{12}; P(\text{not Jide}) = \frac{11}{12}\) \(P(Atu) = \frac{1}{6}; P(\text{not Atu}) = \frac{5}{6}\) \(P(Obu) = \frac{1}{8}; P(\text{not Obu}) = \frac{7}{8}\) \(P(\text{only one of them}) = P(\text{Jide not Atu not Obu}) + P(\text{Atu not Jide not Obu}) + P(\text{Obu not Jide not Atu})\) = \((\frac{1}{12} \times \frac{5}{6} \times \frac{7}{8}) + (\frac{1}{6} \times \frac{11}{12} \times \frac{7}{8}) + (\frac{1}{8} \times \frac{11}{12} \times \frac{5}{6})\) = \(\frac{35}{576} + \frac{77}{576} + \frac{55}{576}\) = \(\frac{167}{576}\)
