Each day Carmen Sandiego is in city A B or C and travels to

Each day, Carmen Sandiego is in city A, B, or C and travels to a different city at most, once. If she is in city A, she travels randomly to another city. If she is in city B, she is as likely to stay as to leave, but if she leaves B then each other city is an equally likely destination. If she is in city C, she is equally likely to stay as to leave, but she does not travel to B. a. Set up the transition probability matrix for Carmen Sandiego’s travels. b. If Carmen Sandiego is in city A, find the probability that she is in city A two days later. c. If Carmen Sandiego is equally likely to start in any of the three cities, find the probability she is in city B after two days.

Solution

The above matrix is the required transition matrix.

b)

Required probability = 0.5*0.25+0.5*0.5 = 0.375

c) Required probability

=(1/3)*(0.5*0.5+0.5*0)+(1/3)*(0.5*0.5+0.25*0.5+0.25*0)+(1/3)*(0.5*0.5+0+0.5*0)

=0.2916