Mary is organizing a special outdoors show which will take place on August 15, the show will loose $20,000; if it is sunny on August 15, the show will earn $15,000. Historically, the likelihood of it raining mid-August is 27%. Suppose that today is July 31. Mary has the option of canceling the show by the end of the day on July 31, but if she does the show will then loose her $1000 deposit on the facilities.
a) What is Mary's optimal decision strategy?
b) Suppose that Mary can also cancel the show on August 14, but if she waits until then to do so, she must pay a fee of $10000. The advantage of waiting until August 14 is that she can listen to the weather forecast for the next day on the local news station. According to the station records, the weather was forecast to be sunny 90% of the days in mid-August the previous years. Also, when the weather was forecast to be sunny, it turned out to be sunny 80% of the time. When the weather was forecast to be rainy it turned out to be rainy 90% of the time. What is Mary's optimal decision strategy in this case?