Tennis tournament probability question!

eeay17

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Jul 10, 2017
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Hi all

I just joined this forum as I was looking for help with a probability question that I can't figure out the answer to:

If you have 64 players in an open tennis draw, and 16 of those players are seeded (i.e. Cannot be drawn against each other in round 1) then what is the probability that a random unseeded player is drawn against a seed in the first round?

My theory is that it is 1/3. This is because the 16 seeded players enter the draw, leaving 48 unseeded players to be drawn. Therefore the chances are 16/48 that the remaining unseeded players are drawn against a seed.

However, my friend says that that is conplicating it. He says that since 16 of the 32 round 1 matches have a seed in it, the chances are simply 1/2 of meeting a seed.

I disagree but wondered if anyone would be able to explain if either of the above two options is correct, or if we are both wrong.

Any help appreciated!

eeay17
 
You are not over-complicating it. You're just counting it wrong.

There are 16 seeded players. They will need an opponent. This clears up 16 games.
The other 16 games are populated by unseeded players. This clears up the other 16 games.

When you said 16/48, you are assuming that 32 unseeded players have no opponent at all and we play 48 games in the first round.
You should have said 16 games / 32 games, not 16 players / 48 players.

Good try, though.
 
Hello, thanks for replying.

So are you saying that it is 1/2?

I wasn't assuming the other games had no one in it. Those were the games that were contested by two unseeded players. Making up the total of 48 (when you take into account the 16 who are playing seeds). Therefore the actual result is that of the 48 total unseeded players, 16 face seeds and 32 do not. Which would make the chances 1/3, no?

Eeay17
 
You can think of it two ways.

16 games have ONE seeded player vs ONE Unseeded Player.
16 games have TWO unseeded players.

If you are a seeded player, your probability of facing a seeded opponent in the 1st round is 0.
If you are an unseeded player, your probability of facing a seeded opponent in the 1st round is 1/3.
1/2 of the GAMES have a seeded player.

Just four Players with one seeded

Seed1
UnSeed1
UnSeed2
UnSeed3

Two Games

1) Seed1 vs UnSeed2
2) UnSeed1 vs UnSeed3

The probability of a GAME having a seeded player is 1/2.
The probability of an unseeded player facing a seeded player 1/3.

Can you both be right and we can all get along?
 
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