3. R programming: Suppose we have two separate bags of balls. Bag A has N number of balls in it, some white some black but we don't know how many of each color. Bag B has K white ball(s) and K, black ball(s). You draw R number of balls from Bag A and move them to Bag B. Then, you draw T balls sequentially from Bag B. Suppose the sequence of the these balls turns out to be [S, S2,..., ST]. We are interested in the composition of balls in Bag A. List your hypotheses and count up all the ways the observed data can happen. Which hypothesis would you believe more? [30 points] (a) Write a code to to calculate the number of ways the observed sequence [S, S2,..., ST] can happen for each hypothesis. Your function should work for any value of N, Kw, K, R, T and for any sequence of balls [S1, S2,..., ST]. [R coding only] [20 points] (b) Which hypothesis is most likely when N = 20, Kw = 10, K = 10, R = 5 and the observed sequence is [W, B, B, W, B, W]. [10 points]