$\begin {array} {1 1} (A)\;\large\frac{1}{4} & \quad (B)\;\large\frac{5}{8} \\ (C)\;\large\frac{1}{2} & \quad (D)\;None\: of \: these \end {array}$

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The man has to win atleast 4 times.

$ \therefore $ The required probability

$ = 7C_4 \bigg( \large\frac{1}{2} \bigg)^4 \bigg( \large\frac{1}{2} \bigg)^3 + 7C_5 \bigg( \large\frac{1}{2} \bigg)^5 \bigg( \large\frac{1}{2} \bigg)^2 +7C_6 \bigg( \large\frac{1}{2} \bigg)^6 \large\frac{1}{2} + 7C_7 \bigg( \large\frac{1}{2} \bigg)^7$

$ = ( 7C_4+7C_5+7C_6+7C7 ). \large\frac{1}{2^7}$

$ = \large\frac{6^4}{2^7}$

$ = \large\frac{1}{2}$

Ans : (C)

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