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.*

## 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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