Consider a sequence consisting of n 1's and m 0's. Suppose all such sequences

are equally likely. We define a run of 1's to be a consecutive string of 1's - e.g., the string

{1, 1, 1, 0, 1, 1, 0, 0, 1, 0} has 3 runs of 1's in it. Compute the expected number of runs of 1's in

the string of n+m symbols. Compute the expected number of runs of any type (1's or 0's), too.