Formulate each of the following as probability models, stating all your assumptions, and use the probability model to answer the questions.

a. Aliens can be friendly or not; 75% are friendly. Friendly aliens arrive during the day 90% of the time, while unfriendly ones always arrive at night. If an alien arrives at night, how likely is it to be friendly?

b. Half of all monsters live in attics, while the rest live in basements. While 80 % of all monsters are fuzzy, all attic-living monsters are fuzzy. What is the probability that a basement-living monsters is fuzzy?