1. **Problem statement:** Find the probability that (i) only one of Mutola or Murumbi is selected, and (ii) none of them is selected, given: - Probability of selecting Mutola $= \frac{7}{8}$ - Probability of selecting Murumbi $= \frac{9}{10}$ 2. **Step 1: Define probabilities of not selecting each person.** - Probability of not selecting Mutola $= 1 - \frac{7}{8} = \frac{1}{8}$ - Probability of not selecting Murumbi $= 1 - \frac{9}{10} = \frac{1}{10}$ 3. **Step 2: Calculate probability that only one is selected.** This means either Mutola is selected and Murumbi is not, or Murumbi is selected and Mutola is not. $$P(\text{only one selected}) = P(M) \times P(\text{not } M_u) + P(\text{not } M) \times P(M_u)$$ 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: $$= \frac{\cancel{16}^{2} \times 8}{\cancel{80}^{10} \times 8} = \frac{2}{10} = \frac{1}{5}$$ 4. **Step 3: Calculate probability that none is selected.** $$P(\text{none selected}) = P(\text{not } M) \times P(\text{not } M_u) = \frac{1}{8} \times \frac{1}{10} = \frac{1}{80}$$ **Final answers:** - (i) Probability only one is selected $= \frac{1}{5}$ - (ii) Probability none is selected $= \frac{1}{80}$