Frank and Joe are playing ping pong. For each game, there is a 30% chance that Frank wins and a 70% chance that Joe wins. During a match, they play games until someone wins a total of 21 games. What is the expected value of number of games played per match?
Frank and Joe are playing ping pong. For each game, there is a 30% chance that Frank wins and a 70% chance that Joe wins. During a match, they play games until someone wins a total of 21 games. What is the expected value of number of games played per match?
The correct option is A 30
Approach 1
The expected value of the ratio of Frank's to Joe's score is 3:7, so Frank is
expected to win 3 games for each of Joe's 7. Extending the same ratio, 3:7 = 9:21. Thus the expected number of games in a match is 30.
Approach 2- Reverse Gear Approach
The ratios imply that Frank wins 7 out of 10 matches and Joe wins 3 out of 10 matches. Total number of matches = 710xN + 310xN (N is the number of matches possible)
Look for a multiple of 10 in the answer options. You can mark option (a) directly
30
Approach 1
The expected value of the ratio of Frank's to Joe's score is 3:7, so Frank is
expected to win 3 games for each of Joe's 7. Extending the same ratio, 3:7 = 9:21. Thus the expected number of games in a match is 30.
Approach 2- Reverse Gear Approach
The ratios imply that Frank wins 7 out of 10 matches and Joe wins 3 out of 10 matches. Total number of matches = 710xN + 310xN (N is the number of matches possible)
Look for a multiple of 10 in the answer options. You can mark option (a) directly
