Probability

There are total 24 possibilities.

For A, if he gets 3 or 4 marks, he should win

if he gets 2 marks, then he will win except B gets 4 marks

if he gets 1 marks, then he can not win except B, C, D gets 2,3,4 marks

P(A will be the final winner)

= (6 + 6 + 4 + 5)/24

= 22/24

= 11/12

Similarly, P(B will be the final winner)

= 2/24

= 1/12

2011-12-29 12:28:50 補充：
Sorry. P(A will be the final winner)

= (6 + 6 + 4 + 1)/24

= 17/24

total probabilities : 4! = 24


(1) Probability of A be the final winner :

If he gets the score 4 or 3 in final game -- total : 6 x 2 = 12

If he gets the score 2, then B mustn't get the score 4 -- total : 4

If he gets the score 1, then B/C/D must get the score 2/3/4 respectively -- total : 1

the chance : (12+4+1)/24 = 17/24


(2) Probability of B be the final winner :

He must get the score 4 and A gets score 1 -- total : 2

the chance : 2/24 = 1/12

how about if A, B, C score 11 after final game? also consider A as a winner of the game?
A = 10 + 1
B = 8 + 3
C = 7 + 4
D = 1 + 2