A chess game between two grandmasters \( X \) and \( Y \) is won by whoever first wins a total o...

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A chess game between two grandmasters \( X \) and \( Y \) is won by whoever first wins a total of two games. \( X \) s chances of
\( \mathrm{P} \) winning, drawing or loosing any particular game are \( a, b \) and

W \( c \), respectively. The games are independent and \( a+b+c=1 \)
The probability that \( X \) wins the match, is
(a) \( \frac{a^{2}(a+2 c)}{(a+c)^{3}} \)
(b) \( \frac{a^{3}}{(a+c)^{3}} \)
(c) \( \frac{a^{2}(a+3 c)}{(a+c)^{3}} \)
(d) \( \frac{c^{3}}{(a+c)^{3}} \)
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