You are not logged in.
Pages: 1
Problem 4
In a university games tournament, 64 students are about to participate in a chess
knockout competition.
The first round consists of 32 games, with two students per game.
The 32 winners of the first round get to play in the second round, which consists of 16
games, and so on, until an overall winner is declared in the sixth round.
(In the case of a draw on any game, a coin is tossed to determine the winner.)
(a) In how many different ways can the 64 participating students be paired up
on the first round?
(Do not consider the order in which students can be paired up.)
(b) Suppose that the 64 participating players are of equal ability,
and pairing up is purely random on each round.
Find the probability that Eva and Brett (two of the 64 students)
will get to play each other at some stage during the knockout competition.
Offline
For (a) No. of combinations in first round is 64C2 but one draw is 32 pairs.
the no. of ways in which draw is made is 64C2/32=63
In subsequent rounds it will be 31,15,7,3 and 1
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
Offline
(b) p1=prob. Eva & Brett meeting in 1st round=1/63
q12=prob. of both going to 2nd round=62/63*1/4 (factor 1/4 is for both to win their games)
p2=prob. Eva & Brett meeting in 2nd round= q12*1/31
q23=prob. of both going to 3rd round=q12*30/31*1/4
p3=prob. Eva & Brett meeting in 3rd round= q23*1/15
q34=prob. of both going to 4th round=q23*14/15*1/4
p4=prob. Eva & Brett meeting in 4th round= q34*1/7
q45=prob. of both going to 5th round=q34*6/7*1/4
p5=prob. Eva & Brett meeting in 5th round= q45*1/3
q56=prob. of both going to 6th round=q45*2/3*1/4
p6=prob. Eva & Brett meeting in 6th round= q56
P=total prob. of Eva & Brett meeting in the tournament=p1+p2+p3+p4+p5+p6
Last edited by thickhead (2016-04-17 21:15:55)
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
Offline
Pages: 1