Using the results from (2)-(b) and (2)-(c), derive |S|, that is the number of possible draws of 8 games?

Part A 16 teams are involved in a soccer tournament. We consider two types of tournaments: (1) There is a group stage: the teams are split into four groups of four teams G1, G2, G3 and G4. In each group, the teams play one against each other and are finally ranked according to their results. For (i, r) ∈ {1, . . . , 4} 2 , we denote by Gi(r) the team finishing at the r-th position in group Gi . The first two teams go through the second stage and the last two are eliminated. (a) For a specific group, how many possible final rankings can be observed? (b) For a specific group, how many pairs of teams can go through? (For two teams T1, T2, {T1, T2} and {T2, T1} are the same pair.) The second stage consists of a series of knock–out rounds which end by a final between two teams. More precisely, the quarter–final consists of the four games: Quarter Final (QF) QF#1 QF#2 QF#3 QF#4 Configuration G1(1) vs G2(2) G1(2) vs G2(1) G3(1) vs G4(2) G3(2) vs G4(1) (c) How many possible last eight configurations can be observed? [15 pts] (2) There is no group stage and 8 games (Game #1, …, Game #8) are drawn at random from the initial pool of 16 teams. We are interested in finding the number of possible draws of 8 games. We consider in this Question that the ordering in the game does not matter i.e. for two teams T1 and T2, the game T1 vs T2 is the same as T2 vs T1. The draw takes the form of a series of 7 draws without replacement, whereby two teams are selected from the pool of available teams, drawing in turns Game #1, …, Game #8. (a) The random experiment consists of the random draw of 8 games. Assign a probability space, that is a sample space S, an event space E and a probability measure P to this random experiment. (b) How many possible games can be formed for Game #1? (c) Game #1 has been drawn, how many possible games can be formed for Game #2? (d) Using the results from (2)-(b) and (2)-(c), derive |S|, that is the number of possible draws of 8 games? [hint: think of a decision tree.] (e) The Republic of Ireland and Germany are 2 of the 16 teams involved in the tournament. Using the previous questions, • how many possible draws feature the game Republic of Ireland vs Germany at Game #1? • how many possible draws feature the game Republic of Ireland vs Germany at Game #2?

Order a unique copy of this paper
(550 words)

Approximate price: $22

Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more

Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
$26
The price is based on these factors:
Academic level
Number of pages
Urgency

Order your stats paper today and save 10% with the discount code SPSSCOVID10