英語翻譯
In the UEFA Euro 2004 playoffs draw 10 national football teams were matched in
pairs.A lot of people complained that “the draw was not fair,” because each strong
team had been matched with a weak team (this is commercially the most interesting).
It was claimed that such a matching is extremely unlikely.We will compute the
probability of this “dream draw” in this exercise.In the spirit of the three-envelope
example of Section 2.1 we put the names of the 5 strong teams in envelopes labeled
1,2,3,4,and 5 and of the 5 weak teams in envelopes labeled 6,7,8,9,and 10.
.We shuffle the 10 envelopes and then match the envelope on top with the next envelope,
the third envelope with the fourth envelope,and so on.One particular way a “dream
draw” occurs is when the five envelopes labeled 1,2,3,4,5 are in the odd numbered
positions (in any order!) and the others are in the even numbered positions.