1. **State the problem:** We are given conditional probabilities of rain on consecutive days and the probability of rain on Monday. We need to estimate the probability of rain on Wednesday. 2. **Given data:** - $P(\text{rain on next day} | \text{rain today}) = 0.8$ - $P(\text{rain on next day} | \text{no rain today}) = 0.6$ - $P(\text{rain on Monday}) = 0.7$ 3. **Define variables:** Let $R_n$ be the event it rains on day $n$. We want $P(R_{Wednesday})$. 4. **Calculate $P(R_{Tuesday})$ using total probability:** $$ P(R_{Tuesday}) = P(R_{Tuesday}|R_{Monday})P(R_{Monday}) + P(R_{Tuesday}|\neg R_{Monday})P(\neg R_{Monday}) $$ Substitute values: $$ P(R_{Tuesday}) = 0.8 \times 0.7 + 0.6 \times (1 - 0.7) = 0.8 \times 0.7 + 0.6 \times 0.3 $$ $$ = 0.56 + 0.18 = 0.74 $$ 5. **Calculate $P(R_{Wednesday})$ similarly:** $$ P(R_{Wednesday}) = P(R_{Wednesday}|R_{Tuesday})P(R_{Tuesday}) + P(R_{Wednesday}|\neg R_{Tuesday})P(\neg R_{Tuesday}) $$ Substitute values: $$ P(R_{Wednesday}) = 0.8 \times 0.74 + 0.6 \times (1 - 0.74) = 0.8 \times 0.74 + 0.6 \times 0.26 $$ $$ = 0.592 + 0.156 = 0.748 $$ 6. **Final answer:** The estimated probability that it will rain on Wednesday is approximately **0.748** or **74.8%**. This uses the law of total probability and conditional probabilities to propagate the chance of rain day by day.