World Cup Direct Qualifying
In the World Cup, the 32 participating teams have been divided into 8 groups.
A team plays only 1 league match with each of the other 3 teams in its group.
A Win gives the team 3 points, a Draw gives the team 1 point; a Loss brings no p
No league match is abandoned.
From each league, 2 teams will qualify to play in the next round, based on the p
oints in their group.
A team is said to qualify "directly", if it has the highest or the second highes
t points in the league.
If there is a tie for the highest points between 2 teams, both will qualify "dir
In all other cases , other complex factors like goals scored for, goals scored a
gainst, etc. are considered,
so that qualification is not "direct".
Suppose the initial Points Table looks like:
Team No. of Games Played Won Draw Loss Points
A - - - - -
B - - - - -
C - - - - -
D - - - - -
What is the probability that
[I asked a few clarifying questions of Sudipta and learned we should
assume that each team is of equal skill, so the outcome of any one game
is equally likely to be a win, draw, or loss for a particular team.
Sudipta feels you can just analyze the results on all the possible
Point Tables. I feel you have to start at the game level for a pure
analysis. The analysis here is for JUST the 6 games among 4 teams and
finding the obvious top 1 or 2 among those 4 teams. - KD]
Team A will qualify "directly"?
Both Team A and Team B will qualify "directly"?
Source: Reader Sudipta Das
Mail to Ken