Question $1(12$ points$)$:

Maria, a professional athlete, trains for triathlons and needs to practice cycling every day during the summer. There are two tracks available for her training: an outdoor track that she can use for free on sunny days, and an indoor velodrome which charges for entry. At the beginning of the summer, Maria has the option of purchasing a $$100$ season pass for the indoor velodrome, which would allow her unlimited access throughout the entire summer. If she does not purchase the season pass, she must pay $$20$ each time she uses the velodrome. Historical weather data suggest that there is a $60\%$ chance the summer will be sunny, resulting in an average of $6$ rainy days during the $90$ days of summer $($and thus $6$ days of needing the indoor track$),$ and a $40\%$ chance that the summer will be rainy, resulting in about $30$ days of the $90$ days of summer requiring the indoor track.

Before the summer begins, Maria has the option of buying a long$-$range weather forecast for $$20.$ The forecast depends on the number of rainy and sunny days in the upcoming $90$ days in weather maps.

Maria's goal is to minimize his total expected cost for summer training. Should Maria buy the season pass? Should he pay for the long$-$range forecast? Also, calculate EVSI and EVPI

Suppose the EVPI is equal to Zero, what does this mean?