A student is deciding whether to go to a party or stay home. For this problem, we will use generic utility units, utils, to quantify the student's enjoyment. If the student decides to go to the party, there is a 40% chance that it will be awesome, and the student will get 10 utils. By contrast, if the party is boring (not awesome), then the student will get no utils. If the students decides to stay home, then the student will get 3 utils.

 (a)  Calculate the expected utils the student gets for going to the party, and determine whether the student should go to the party or stay home based upon prior probabilities. The student may also text his friend, who is already at the party, to see how it's going. However, he and his friend don't always agree on the awesomeness of parties. Specifically, if the student thinks a party is awesome, there is a 80% chance that his friend agrees. If the student thinks a party is boring, then there is an 10% chance that his friend disagrees and thinks it is in fact awesome. 

(b) Calculate the probability that the student's friend will think that the party is awesome. [Hints:: You need to use Law of Total Probability here] 

(c) Given that the student's friend thinks that the party is awesome, calculate the probability the student agrees that the party is awesome. [Hints:: You need to use Bayes' Theorem here] 

(d)Given that the student's friend thinks that the party is awesome, calculate the expected utils the student gets for going to the party. The student is considering employing a policy based upon his friend's text; he will go to the party if the friend says that it is awesome, and he will stay home if his friend says it is boring. In addition, the student's friend never responds immediately to texts, which costs the student 1 util for having to wait around for his friend's responding text. Eventually, the student gets 203 50 utils after hearing his friend's text. 

(e) Should the student wait for a response to his friend's text or just make the decision from part (a) without waiting?