Alice is taking a probability class and at the end of each week

she can be either up-to-date or she may have fallen behind. If she is up-to-date in

a given week, the probability that she will be up-to-date (or behind) in the next

week is 0.8 (or 0.2, respectively). If she is behind in a given week, the probability

that she will be up-to-date (or behind) in the next week is 0.6 (or 0.4, respectively).

Alice is (by default) up-to-date when she starts the class. What is the probability

that she is up-to-date after three weeks?

This is a probability problem from Bertsekas and Tsitsiklis' textbook. The answer given is that

P(U3) = P(U2)*P(U3 |U2) P(B2)*P(U3 |B2) = P(U2) · 0.8 P(B2) · 0.4

However, the answer I'm finding is

P(U3) = P(U2)*P(U3 |U2) P(B2)*P(U3 |B2) = P(U2) · 0.8 P(B2) · 0.6

Am I missing something or did they make a mistake in the textbook?