You are in a tennis club with two other members. One of them, Roger (think Federer) is a really good tennis player, and you have a 0.1 probability of winning a match against him. The other player is Joe (think average). He is a pretty good tennis player, and you have a 0.5 probability of winning a match against him.
Now, you are given a choice of the following two sequences of matches:Roger, Joe, RogerorJoe, Roger, JoeThe rule is that you will collect a prize if and only if you win at least two games in a row among your set of three matches. (Note: winning two out of three is not enough; you have to win at least two consecutive matches.)
QUESTION 1) Which of these two schedules (RJR or JRJ) offers you the better chance of collecting a prize?
QUESTION 2) What is the expected number of wins for you in the sequence RJR? In the sequence JRJ?