(20 point) Uber faces tough competition from Lyft. Historical data shows that weather conditions significantly influence ride demand. The probability of a rainy day is , and the probability of a snowy day is . The weather can be sunny, rainy, or snowy, leading to different demand levels for rides. Weather Conditions and Demand for Rides: - Sunny Weather: High demand - Rainy Weather: Medium demand - Snowy Weather: Low demand Lyft's Discount Strategy: - When demand is high (sunny weather), Lyft offers discounts with a probability of 1/6 - When demand is medium (rainy weather), Lyft offers discounts with a probability of 1/3 - When demand is low (snowy weather), Lyft offers discounts with a probability of 1/2. Uber's Daily Profits: - If the weather is sunny and demand is high: Uber's profit is $300 when Lyft offers discounts. Uber's profit is $900 when Lyft does not offer discounts. - If the weather is rainy and demand is medium: Uber's profit is $100 when Lyft offers discounts. Uber's profit is $400 when Lyft does not offer discounts. - If the weather is snowy and demand is low: Uber loses $500 (profit = -$500) when Lyft offers discounts. Uber loses $100 (profit = -$100) when Lyft does not offer discounts. (a) What is the probability that the demand for rides is high