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Question

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?


  1. 30

  2. 28

  3. 27

  4. 29


Solution

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

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