Math Is Fun Forum

Janiffer

Member

Registered: 2008-04-26

Posts: 12

stats!!!!

in a uni games tournament, 64 students are about to participate in a chess knockout tournament.

The  first round consists of 32 games, with 2 students per game.

The 32 winners of the first round get to play in the 2nd round, which consists of 16 games, and so on, until an overall winner is declared in the 6th round.

(in the case of a draw n any game, a coin is tossed to determine the winner)

a) In how many differrent ways can the 64 participating students be paired up on the first round? (order not required)

b)Suppose the 64 players are of equal ability, and pairing up is purely random on each round.

Find the probability that EVA and BRETT( 2 of the 64 students) will get to play each other at some stageduring the knockout competition....

Can some please help me with this question.....

Thanks loads!!!!!!!!!!!

( working please;))

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: stats!!!!

a)

The first player has 63 possible partners that could be paired up with them.
After this pairing has been decided, there are 62 unassigned players left.
Choose one of those, and then there are 61 possible partners for them.
Choose one of the 60 remaining, and there are 59 possible partners for them.

So overall, there are 63*61*59*57*...*5*3*1 possible setups (sometimes known as 63!!).

b)

Work out the probability of them meeting at each round.
In round 1, Brett and Eva are both definitely still in the tournament. Brett has 63 possible partners, so there's a 1/63 chance that they meet there.

In round 2, they both have a 1/2 chance of still being in (so 1/4 altogether). Assuming they are both in, Brett has 31 possible partners and so there's a 1/31 * 1/4 = 1/124 chance of them meeting.

In round 3, the probability is 1/15 * 1/16 = 1/240

Work out the probabilities of them meeting in the quarters, semis and final and then add all the probabilities together to get the final answer.

Edit: See Jane's post for a bit I missed

---

Why did the vector cross the road?
It wanted to be normal.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: stats!!!!

Mathsy, did you leave something out?

The probability that they will meet in the 1st round is

.

The probability that they will meet in the 2nd round is

Similarly the probability that they will meet in the 3rd round is

The probability that they meet in the quarterfinals is

Hence the answer to part (b) is

Janiffer

Member

Registered: 2008-04-26

Posts: 12

Re: stats!!!!

thnk u....