Problem #WSP-000413

Problems Probability and statistics

Problem

A city planning committee contains a proportion \(p\) of members of the Even party, who never change their minds about anything, and a proportion \(1-p\) of members of the Odd party who change their minds completely at random (with probability \(r\)) between successive votes on the same issue. A randomly chosen committee member is noticed to have voted twice in succession in the same way. What is the probability that this member will vote in the same way next time?