Solution:
(i) We know that,
The probability of winning of A + Probability of losing of A = 1
And,
Probability of losing of A = Probability of winning of B
Therefore,
Probability of winning of A + Probability of winning of B = 1
0.83 + Probability of winning of B = 1
Hence, probability of winning of B = 1 – 0.83 = 0.17
(ii) We know that,
Probability of winning of B + Probability of losing of B = 1
And, probability of losing of B = Probability of winning of A
Therefore,
Probability of winning of A = 0.49
subject to the constraints: 
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is squal to
. prove that 
defined by 
, if 
if 
then 
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and 
, then 