In your tennis club there are two other members. One of them is a very good player. His name is Roger (think Federer) and you have a 0.1 probability of winning a match against him. The other player is Joe (think average). He is a decent tennis player and you have a 0.4 probability of winning a match against him. In a tennis tournament, you have two choices for the sequence of matches: Roger, Joe, Roger or Joe, Roger, Joe To get a prize in the tournament you need to win at least two matches in a row among your set of three matches. (Note: this does not mean winning two out of three matches; you have to win at least two consecutive matches.)
4a. Which of these two schedules (RJR or JRJ) gives you the better chance at a prize?
4b. What is the expected number of wins for you in the sequence RJR? In the sequence JRJ?
For Part A, I just multiplied the probabilities of each comination of 3 that includes two consecutive wins (w,w,l), (l,w,w), (w,w,w). For RJR, this came out to be 0.076. For JRJ I got 0.064.
For Part B, I'm a little stuck. I started calculating the expected number of winning games like so:
0 games won * (0.9*0.6*0.9) = 0
1 game won * (0.1*0.6*0.9 + 0.9*0.4*0.9 + 0.9*0.6+0.1) = 0.432
2 games won * (0.1*0.4*0.9 + 0.9*0.4*0.1 + 0.1*0.6+0.1) = 0.156
3 games won * (0.1*0.4*0.1) = 0.012
0+0.432+0.156+0.012 = 0.6
And the same for the JRJ order. Is this correct though?