Q.11 [4] Suppose that P(A ) = . P(B)=-, and P(AnB)= 3. 18 a. Are events A and B dependent or independent? Why? b. Determine P(B/ A). I C. Determine P(A / B).Q.12 Consider the Markov chain below. B 1/2 1/2 1/2 1/2 A C 3/4 1/4 What is the transition matrix?Q.15 [8] Suppose there are two cities, X and Y. Every year, . 70% of the people from X stay in X, the remaining 30% move to Y. . 40% of the people from Y stay in Y, the remaining 60% move to X. The initial populations of X and Y are 330 and 220, respectively. (a) What is the initial probability vector? (b) What is the transition matrix? (c) After one year of time what is the population (in percent) in city X? (d) After a long period of time what is the population (in percent) in city X