[10pts] Mary is a scientist considering two mutually exclusive and collectively exhausting hypotheses: H and H. The (prior) probability of H is 0.25. Mary has access to evidence E. Assuming H is true, the probability of evidence E occurring is 0.6 (i.e., the likelihood of E on H is 0.6). Assuming H is true, the probability of E is 0.2. (a) What is the (posterior) probability of H given E? And what is the probability of H given E? Show your work! (b) Suppose some additional evidence E 0 comes in, where the probability of E 0 occurring given both H and E is 0.3 whereas the probability of E 0 given both H and E is 0.1. What is the probability of H given both E and E 0 ? Show your work!