1. A TV provider offers subscribers some channel packages: news, movies, and a combination package with both. Let N denote the event that a subscriber purchases a news package, and let M denote the event that a subscriber purchases the movies package. Based on the TV provider's history of selling packages, we have the following probabilities: P(N) = 0.5, P(M) = 0.3. Should there be another event in the hypothesis space? If so, what is its probability and why did you choose that value?

2. In a series of NBA playoffs, the Los Angeles Lakers' likelihood of winning a game against Celtics, Nets, Bucks, and Warriors is given by P(Celtics) = 0.1, P(Nets) = 0.7, P(Bucks) = 0.3, P(Warriors) = 0.2. What is the total probability? What is the normalized probability? Show your work.

3. Check the values that cannot be a probability:

0.5

1.001

0

1

30%

-0.004

4. A researcher considers the role of a human's intuitive understanding of physics in a person's moral judgment. Explain why this could be a reasonable assumption.

5. What is the indirectness of human speech? Why are humans capable of speaking indirectly?