A non-angler, curious to know what counts as a good day of fishing (F) at the lake and puzzled by the phenomenon that it can sometimes be a good day even when no fish are caught, decides to create a naive Bayes model with F as the Boolean class variable and three features: whether it rained (R), how many fish were caught (C) with values {none, some, lots}, and whether it was windy (W). A naive Bayes net is shown in the Figure below W C F PR b. Derive symbolic expressions for the following probabilities in terms of P(R|C), P(C|F), P(W|F), and P(F): I. P(R) II. P(R|C,W) III. P(R,C,W | F)