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.
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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.
1 comment:
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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