Parliament contains a proportion p of Labour Party members, incapable of changing their opinions about anything, and 1 – p of Tory Party members changing their minds at random, with probability r,...

Extracted text: Parliament contains a proportion p of Labour Party members, incapable of changing their opinions about anything, and 1 – p of Tory Party members changing their minds at random, with probability r, between subsequent votes on the same issue. A randomly chosen parliamentarian is noticed to have voted twice in succession in the same way. Find the probability that he or she will vote in the same way next time.