2. Tom is deciding if a new medicine is very effective (VE), somewhat effective (SE), or not effective (NE). His initial belief is that the probability the medicine is very effective is .5, the probability the medicine is somewhat effective is .25, and the probability that the medicine is not effective is .25. If the medicine is very effective, it will treat the disease with probability .9 (and not treat it otherwise). If the medicine is somewhat effective, it will treat the disease with probability .6, and if it is not effective, it will treat the disease with probability .3. Suppose that Tom sees 4 patients (inorder) with the following outcomes: treated, not treated, treated, treated. (a) If Tom is not biased, what is his updated belief that the medicine is very effective? (b) If Tom believes in the law of small numbers, what is his updated belief that the medicine is very effective? Let N=10, m=5. (c) If Tom believes in the law of small numbers, what is his updated belief that the medicine is very effective? Let N=10, m=3. (d) Explain the relationship between your ndings in (a), (b), and (c)