$\begin {array} {1 1} (A)\;\large\frac{1}{2} & \quad (B)\;\large\frac{1}{8} \\ (C)\;\large\frac{3}{8} & \quad (D)\;None\: of \: these \end {array}$

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Let X denote the number of tails. Then X is a binomial variate with parameters

$ n = 100\: \: \: \: P = \large\frac{1}{2}$

$ \therefore P(x=r)=100C_r \bigg( \large\frac{1}{2} \bigg) ^{100}\: \: \: \: r=0,1,2,.....100$

Required probability = $ P(x=1) +P(x=3)+.....P(x=99)$

$ = \bigg( \large\frac{1}{2} \bigg)^{100} [100C_1+100C_3+.....+100C_{99} ]$

$ \large\frac{1}{2^{100}} [2^{99} ]$

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

Hence (A)

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