We can number the states as follows:

1: jetty   2: swimming area;   3: volleyball play area

With this numbering, the transition matrix is

P = 1 0 0 0 1/2 1/2 1/6 1/3 1/2 .   (Note that the fractions not specified in the question were computed to make the rows add to 1.)

Also, we have the distribution vector

v = [0   1,200   0].

The distribution at 2 pm. (after 2 one-hour steps) is given by

v P2 = [ 0  1,200   0 ] 1 0 0 0 1/2 1/2 1/6 1/3 1/2 1 0 0 0 1/2 1/2 1/6 1/3 1/2 = [ 100   500   600 ] .

Thus, there are 100 people at the jetty at 2 pm.

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