You are evaluating two mutually exclusive hypotheses H1 and H2 in light of evidence E, and your probability assignment is as follows:

Prior probabilities: P(H1)= .2 and P(H2)= .5

Likelihoods: P(E|H1)= .8 and P(E|H2)= .4

1. What is the Bayes Factor in this case?
2. Which of the two hypotheses, H1 and H2, does evidence E favor in this case?
3. What is the prior probability of the catch-all (neither H1 nor H2) hypothesis HC in this case?

Part 2

Suppose further (for the sake of the argument) that you assign the likelihood P(E|HC) = .1 to the

catch-all hypothesis HC

1. What is the prior probability of evidence E in this case?
2. What is the posterior probability P(H1|E) of hypothesis H1 given evidence E in this case?