1Extracted text: 2 of 5
Question 1
1. (a) Consider a play-off tournament (where the loser is out,...

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1Extracted text: 2 of 5
Question 1
1. (a) Consider a play-off tournament (where the loser is out, and the winner advances to the next round) with n rounds and
2" players. Two players are chosen at random. Calculate the probability that they play against each other:
(i) in the first round;
(ii) in the final, i.e. the last round;
(iii) in any round.
(b) The number of misprints on a page has a Poisson distribution with parameter A, and the numbers of misprints on different
pages are independent.
(i) What is the probability that the second misprint will occur on page r?
(ii) A proof-reader studies a single page looking for misprints. She catches each misprint (independently of others) with
probability p e [0, 1]. Let X be the number of misprints she catches and let Y be the number she misses. Find the
distributions of the random variables X and Y and show they are independent.

Jisha · Accepted Answer

Question 1
 (a) Consider a play-off tournament (where the loser is out, and the winner advances to the next round) with n rounds and 2" players. Two players are chosen at random. Calculate the probability that they play against each other:
 (i) in the first round;
 (ii) in the final, i.e. the last round; 
(iii) in any round. 
Let  and  be the two players. Given that there are n rounds and  players.
 (i) has been selected in the first round, then there are -1 slots left for . Therefore probability that  and  play against each other in the first round is 
(ii) The probability of winning each player in any match is  Here the players   and  are chosen at random.

2 of 5 Question 1 1. (a) Consider a play-off tournament (where the loser is out, and the winner advances to the next round) with n rounds and 2" players. Two players are chosen at random. Calculate...

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