31. Each element in a sequence of binary data is either 1 with probability p or 0 with probability 1 − p. A maximal subsequence of consecutive values having identical outcomes is called a run. For instance, if the outcome sequence is 1, 1, 0, 1, 1, 1, 0, the first run is of length 2, the second is of length 1, and the third is of length 3.

(a) Find the expected length of the first run.

(b) Find the expected length of the second run.