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Advance Maths Problem 65 Please don’t answer compulsory I will give dislike A tennis tournament is arranged for 2 n players. It is organised as a knockout tournament, so that only the winners in any given round proceed to the next round. Opponents in each round except the final are drawn at random, and in any match either player has a probability 1 2 of winning. Two players are chosen at random before the start of the first round. Find the probabilities that they play each other: (i) in the first round; (ii) in the final round; (iii) in the tournament. Comments Note that the set-up is not the usual one for a tennis tournament, where the only random element is in the first round line-up. Two players cannot then meet in the final if they are in the same half of the draw. Part (i) is straightforward, but parts (ii) and (iii) need a bit of thought. There is a short way and a long way of tackling these parts, and both have merits. It is a good plan to check your answers, if possible, by reference to simple special cases where you can see what the answers should be; n = 1 or n = 2, for example. Interestingly, the answers are independent of the probability that the players have of winning a match; the 2s in the answers represent the number of players in each match rather than (the reciprocal of) the probability that each player has of winning a match. It also does not matter how the draw for each round is made. This is clear if you use the short method mentioned above.

Name: advance maths problem 65 please dont answer compulsory i will give dislike a tennis tournament is arranged for 2 n players it is organised as a knockout tournament so that only the winners in any gi 2
Uploaded: 2023-08-21T18:04:45-08:00
Duration: 7 min 46 s
Channel: Sri K
Description: advance maths problem 65 please dont answer compulsory i will give dislike a tennis tournament is arranged for 2 n players it is organised as a knockout tournament so that only the winners in any gi 2

          Advance Maths Problem 65
Please don’t answer compulsory I will give
dislike
A tennis tournament is arranged for 2 n players. It is organised
as a knockout tournament, so that only the winners in any given
round proceed to the next round. Opponents in each round except the
final are drawn at random, and in any match either player has a
probability 1 2 of winning. Two players are chosen at random before
the start of the first round. Find the probabilities that they play
each other: (i) in the first round; (ii) in the final round; (iii)
in the tournament. Comments Note that the set-up is not the usual
one for a tennis tournament, where the only random element is in
the first round line-up. Two players cannot then meet in the final
if they are in the same half of the draw. Part (i) is
straightforward, but parts (ii) and (iii) need a bit of thought.
There is a short way and a long way of tackling these parts, and
both have merits. It is a good plan to check your answers, if
possible, by reference to simple special cases where you can see
what the answers should be; n = 1 or n = 2, for example.
Interestingly, the answers are independent of the probability that
the players have of winning a match; the 2s in the answers
represent the number of players in each match rather than (the
reciprocal of) the probability that each player has of winning a
match. It also does not matter how the draw for each round is made.
This is clear if you use the short method mentioned above.

Added by Patrick F.

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