Sunday, April 27, 2014

Average number of matches won

In Wimbledon's women's singles tournament there are 128 players. It is a knock-out tournament. I.e. after each round the losers are excluded from the next round.
The first round losers will have a win percentage of 0%.
The overall winner will have a 100% win percentage.

Part A: What's the average win percentage, (assuming the weighting of each player is equal)?

Part B: What's the average win percentage if each player is weighted proportional to how many matches she played?

Level of background mathematics required: high-school.
Difficulty level: straight-forward.

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1 comment:

  1. Philip KinlenApril 28, 2014 at 2:41 AM

    The answers:

    Part A: 30.77%,

    which is:
    1 * (7/7)
    + 1 * (6/7)
    + 2 * (5/6)
    + 4 * (4/5)
    + 8 * (3/4)
    +16 * (2/3)
    +32 * (1/2)
    +64 * (0/1)

    all divided by 128

    Part B: 50.00%
    when every match is equal weighted, the average win percentage is 50%.

    April 28, 2014 at 2:39 AM

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