# Probability in knock-out torunament

#### chrisyuen

1. Homework Statement

Albert, Bobby and six other players take part in a table-tennis knock-out tournament. The winner of each match can proceed to the next round as shown in the following figure and the loser is knocked out. The players are randomly assigned to the eight positions in the first round. Suppose the eight players are equally skillful.

(a) What is the probability that Albert will play Bobby in the first round?

(b) What is the probability that Albert will ever play Bobby in a match during a tournament?

(a) $$\frac{1}{7}$$
(b) $$\frac{1}{4}$$)

2. Homework Equations

Permutation and Combination Formulae

3. The Attempt at a Solution

Part (a), total combinations = $$\frac{8!}{6!}$$ = 56

P = $$\frac{8}{56}$$ = $$\frac{1}{7}$$.

Am I correct?

Part (b), I don't know how can I start this part.

Can anyone tell me how to solve it?

Thank you very much!

#### Attachments

• 13.3 KB Views: 156
Related Calculus and Beyond Homework Help News on Phys.org

"Probability in knock-out torunament"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving