1. **Stating the problem:** We are given that the probability it will rain on any day is $\frac{1}{6}$. We need to find: a. The probability it will not rain on a particular day. b. The probability it will not rain on two particular consecutive days. c. The probability it will not rain on just one of the two particular consecutive days. 2. **Formula and rules:** - The probability of an event not happening is $1 - P(\text{event})$. - For independent events, the probability of both occurring is the product of their probabilities. - For "just one" of two events happening, use the sum of probabilities of each event happening alone minus the probability of both happening (if needed). 3. **Step-by-step solution:** **a. Probability it will not rain on a particular day:** $$P(\text{no rain}) = 1 - P(\text{rain}) = 1 - \frac{1}{6} = \frac{5}{6}$$ **b. Probability it will not rain on two particular consecutive days:** Assuming independence between days, $$P(\text{no rain on day 1 and day 2}) = P(\text{no rain on day 1}) \times P(\text{no rain on day 2}) = \frac{5}{6} \times \frac{5}{6} = \frac{25}{36}$$ **c. Probability it will not rain on just one of the two particular consecutive days:** This means it rains on exactly one day and not on the other. Calculate the probability it rains on day 1 and not on day 2: $$P(\text{rain on day 1 and no rain on day 2}) = \frac{1}{6} \times \frac{5}{6} = \frac{5}{36}$$ Calculate the probability it rains on day 2 and not on day 1: $$P(\text{no rain on day 1 and rain on day 2}) = \frac{5}{6} \times \frac{1}{6} = \frac{5}{36}$$ Add these two mutually exclusive events: $$P(\text{just one day of rain}) = \frac{5}{36} + \frac{5}{36} = \frac{10}{36} = \frac{5}{18}$$ 4. **Final answers:** a. $\frac{5}{6}$ b. $\frac{25}{36}$ c. $\frac{5}{18}$ These probabilities describe the likelihood of no rain on one day, no rain on two consecutive days, and rain on exactly one of two consecutive days respectively.