There are 8 teams A, B, C, D, E, F, G, H. There winning order is A>B>C>D>E>F>G>H. A tournament of cr

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02 Mar 2012 probability

There are 8 teams A, B, C, D, E, F, G, H. There winning order is A>B>C>D>E>F>G>H. A tournament of cricket has to be played between all the teams in knockout manner according to the following rules
1) First we have to make two pools of 4-4 teams
2) In every pool there will be two knockout and one semifinal
3) Final will be played between winner of semifinals of both pools.
If it is given that C team is not reached to the final,
Find the probability of having a final between A and B

OPtion

1) 1
2) 1/2
3) 0
4) 3/5
5) 4/5
6) 2/3
7) 3/4
8) 8/15
9) 1/3
10) none of these

Solution

Total no of matches = (8*7*6*5/4*3*2*1)*3*3/2 = 315
Distribution of matches
A and B in any 1 Pool and C in the other pool: total matches of this type = (5*4/2*1)*3*3 = 90
B and C in any 1 Pool and A in the other pool: total matches of this type = (5*4/2*1)*3*3 = 90
C and A in any 1 Pool and B in the other pool: total matches of this type = (5*4/2*1)*3*3 = 90
A, B and C in the same pool : total matches of this type = 45
In first 90 cases C will reach in the final so these are not possible cases
Other 225 cases are possible for rejecting C before final
But in last 45 cases all are in the same pool so B and C both will be eliminated before final so these are non favorable cases
so probability for the required event = 180/225 = 4/5

Correct Option: 5 Best Solution (1)

~Sandeep~   12 years AGO

Considering C not reaching to finals following two formations are possible fixing A, B & C's position:
1. Pool 1 - AXXX
Pool 2 - BXXX
Number of ways to choose from teams marked as X from other 6 teams= 6C3 = 20
2. Pool 1 - ABCX
Pool 2 - XXXX
Number of ways to choose from teams marked as X from other 5 teams= 5C1 = 5
In formation 1 team A & B both will reach finals whereas in formation 2 only A will reach final but B will not reach final.
Hence probability of having a final between A and B = 20/(20+5) = 20/25 = 4/5 (Option 5)

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