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

$\frac{7}{128}$

The correct answer is Option (2) - $\frac{7}{128}$

P(atleast 8 correct out of 10) = P(8 correct) + P(9 correct) + P(10 correct)

$={^{10}C}_8×(\frac{1}{2})^8(\frac{1}{2})^2+{^{10}C}_9×(\frac{1}{2})^9(\frac{1}{2})+{^{10}C}_{10}×(\frac{1}{2})^{10}$

$=\frac{1}{2^{10}}(\frac{10×9}{2}+10+1)=\frac{56}{2^{10}}=\frac{7}{128}$