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# The probability of guessing correctly atleast 8 out of 10 answers on a true - false examination is :

$\begin {array} {1 1} (A)\;\large\frac{7}{64} & \quad (B)\;\large\frac{7}{128} \\ (C)\;\large\frac{45}{1024} & \quad (D)\;\large\frac{175}{1024} \end {array}$

$P( X \geq 8 ) = 10C_8 \bigg( \large\frac{1}{2} \bigg)^8\bigg( \large\frac{1}{2} \bigg)^2+10C_9 \bigg( \large\frac{1}{2} \bigg)^9\bigg( \large\frac{1}{2} \bigg)+10C_{10}\bigg( \large\frac{1}{2} \bigg)^{10}$
$= \large\frac{1}{2^{10} }(10C_1+10C_1+1)$
$= \large\frac{1}{2^{10} }(45+10+1)$
$\large\frac{7}{128}$
Ans : (B)