Probability (1 Viewer)

[michaeljennings]

A, B, C, D are, in order, the football semifinalists. In the first semifinal A plays B, in the second C plays D. The winner of the first semifinal will play in the final, the loser plays the winner of the second semifinal, an the winner of this match is the other finalist. Assuming that each team has an even chance of winnings each of its matches, what chance has each team of winning the final:
(1) before the first semi-final
(2) after A has defeated B in the first semifinal

My answers were as follows:
(1) A & B = 3/8, C & D = 1/8
(2) A = 1/2, B = 1/4, C & D = 1/8


Could someone please tell me what they get because there are no solutions with this question

 

[OldMathsGuy]

There are 16 different ways how this competition could progress across the four matches with the winners of each match as follows:

A C B A
A C B B
A C C A
A C C C
A D B A
A D B B
A D D A
A D D D
B C A B
B C A A
B C C B
B C C C
B D A B
B D A A
B D D B
B D D D

1) Your solutions are correct.
2) You ignore the final 8 results to again get your correct solutions.

Best Regards
OldMathsGuy

 

[michaeljennings]

There are 16 different ways how this competition could progress across the four matches with the winners of each match as follows:

A C B A
A C B B
A C C A
A C C C
A D B A
A D B B
A D D A
A D D D
B C A B
B C A A
B C C B
B C C C
B D A B
B D A A
B D D B
B D D D

1) Your solutions are correct.
2) You ignore the final 8 results to again get your correct solutions.

Best Regards
OldMathsGuy

Thank you for being the only one to reply =)