1. **Problem statement:** Find the probability that i) only one of Mutola or Murambi is selected, ii) none of them is selected. 2. **Given:** - Probability of selecting Mutola $P(M) = \frac{7}{8}$ - Probability of selecting Murambi $P(N) = \frac{9}{10}$ 3. **Important rules:** - Probability of not selecting Mutola $P(M^c) = 1 - P(M) = 1 - \frac{7}{8} = \frac{1}{8}$ - Probability of not selecting Murambi $P(N^c) = 1 - P(N) = 1 - \frac{9}{10} = \frac{1}{10}$ 4. **Calculate probability that only one is selected:** This means either Mutola is selected and Murambi is not, or Murambi is selected and Mutola is not. $$P(\text{only one}) = P(M) \times P(N^c) + P(M^c) \times P(N)$$ Substitute values: $$= \frac{7}{8} \times \frac{1}{10} + \frac{1}{8} \times \frac{9}{10}$$ $$= \frac{7}{80} + \frac{9}{80} = \frac{16}{80}$$ Simplify fraction: $$= \frac{\cancel{16}^{2} \times 8}{\cancel{80}^{10} \times 8} = \frac{2}{10} = \frac{1}{5}$$ 5. **Calculate probability that none is selected:** $$P(\text{none}) = P(M^c) \times P(N^c) = \frac{1}{8} \times \frac{1}{10} = \frac{1}{80}$$ **Final answers:** - Probability only one is selected: $\frac{1}{5}$ - Probability none is selected: $\frac{1}{80}$