![\[\left( \mathbf{i} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ec4588e8cb8288d41d93726c3b60fee0_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{0}.\mathbf{83}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1e4fcef37405717c20e577f1366ab70a_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{ii} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a4cc96f58fba9e185f598e5aebb7decb_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{0}.\mathbf{49}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c532bc1eecea944e3ba513bc0032287e_l3.png "Rendered by QuickLaTeX.com")
Solution:
![\[\left( i \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c013687aa5dbc1ecafb4bc91b7e8e7fe_l3.png "Rendered by QuickLaTeX.com")
We know that,
The probability of winning of A
![\[+\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-64ad0cf3c89576bab5cc0b95043c42b4_l3.png "Rendered by QuickLaTeX.com")
Probability of losing of A
![\[=\text{ }1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8a57971cb63419909e5e317986f73838_l3.png "Rendered by QuickLaTeX.com")
And,
Probability of losing of A
![\[=\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6b746a84754416d75595916b2050838f_l3.png "Rendered by QuickLaTeX.com")
Probability of winning of B
Therefore,
Probability of winning of A
Probability of winning of B
![\[=\text{ }10.83\text{ }+\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9c30ed55b137f214b826279669a46221_l3.png "Rendered by QuickLaTeX.com")
Probability of winning of B
Hence, probability of winning of B
![\[=\text{ }1\text{ }\text{ }0.83\text{ }=\text{ }0.17\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7f7f2c88067902e35eba8de35248b9a6_l3.png "Rendered by QuickLaTeX.com")
![\[\left( ii \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fb274751d677ea2ebc95af4c2f5fd659_l3.png "Rendered by QuickLaTeX.com")
We know that,
Probability of winning of B
![\[~+\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-623044b2c169e0121f4ca97d88da5aeb_l3.png "Rendered by QuickLaTeX.com")
Probability of losing of B
And, probability of losing of B
Probability of winning of A
Therefore,
Probability of winning of A
![\[=\text{ }0.49\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-86050929748d6697f4ce7b8b99948fbe_l3.png "Rendered by QuickLaTeX.com")
