1. **State the problem:** We want to find the probability that Joss is not late to work given the probabilities related to rain and bus lateness. 2. **Given data:** - Probability it rains: $P(R) = 0.25$ - Probability bus is late if it rains: $P(L|R) = 0.4$ - Probability bus is late if it does not rain: $P(L|R^c) = 0.005$ 3. **Find:** The probability that Joss is not late, i.e., $P(L^c)$. 4. **Use the law of total probability:** $$P(L) = P(L|R)P(R) + P(L|R^c)P(R^c)$$ where $P(R^c) = 1 - P(R) = 1 - 0.25 = 0.75$. 5. **Calculate $P(L)$:** $$P(L) = (0.4)(0.25) + (0.005)(0.75) = 0.1 + 0.00375 = 0.10375$$ 6. **Calculate $P(L^c)$:** Since $P(L^c) = 1 - P(L)$, $$P(L^c) = 1 - 0.10375 = 0.89625$$ 7. **Interpretation:** The probability that Joss is not late is approximately $0.896$ or 89.6%.