Solution:
\[\left( i \right)\]We know that,
The probability of winning of A \[+\]Probability of losing of A \[=\text{ }1\]
And,
Probability of losing of A \[=\] Probability of winning of B
Therefore,
Probability of winning of A \[+\] Probability of winning of B \[=\text{ }10.83\text{ }+\] Probability of winning of B \[=\text{ }1\]
Hence, probability of winning of B \[=\text{ }1\text{ }\text{ }0.83\text{ }=\text{ }0.17\]
\[\left( ii \right)\] We know that,
Probability of winning of B\[~+\] Probability of losing of B \[=\text{ }1\]
And, probability of losing of B \[=\]Probability of winning of A
Therefore,
Probability of winning of A \[=\text{ }0.49\]