is there a method to solve this? 3. (5 marks) Eight tennis players (call them A,

Question

is there a method to solve this?

3. (5 marks) Eight tennis players (call them A,B,C,D,E,G,F,H) are randomly assigned to start positions in a ladder tournament. Initially, position 1 plays position 2, position 3 plays 4, 5 plays 6 and 7 plays 8. Second round has 2 matches: winner of (1,2) match plays winner of (3,4), and winner (5,6) plays winner(7,8). The winners of the two 2nd round matches play each other in the final match. Player A wins against any of the others. Player B always beats any opponent except player A. What is the probability that player B wins the 2nd place trophy in the final match?

Explanation / Answer

Here we have to find the probability that player B wins the second place trophy in the final match. So that means A and B will play the final.It is becuase that if B have to play with A before final, he couldn't be able to play in the final match.

so, Now we can see that if A is in 1 to 4 position, then B must be in 5 to 8 position and similarly, for A is in 5 to 8 position, then B is in 1 to 4 position.

so Total number of position A and B without any constraint is = 8 * 7 = 56

now with the constraint, total number of position A and B can have is.

(i) If A holding position in 1 to 4 then B can hold 5 to 8, total number ofpositions = 4 * 4 = 16

(ii) If A holding psotion in 5 to 8 then B can hold 1 to 4, then total numberof positions = 4 * 4 = 16

so total number of positions = 16 + 16 = 32

so Pr(B will get second trophy) = 32/56 = 4/7

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