The National Weather Service issues precipitation forecasts that indicate the likelihood of measurable precipitation (≥ .01 inch) at a specific point (the official rain gauge) during a given time period. Suppose that if a measurable amount of rain falls during the next 24 hours, a river will reach flood stage and a business will incur damages of $300,000. The National Weather Service has indicated that there is a 30% chance of a measurable amount of rain during the next 24 hours.
a. Construct the probability distribution that describes the potential flood damages.
b. Find the firm's expected loss due to flood damage.