Question

The probability of guessing correctly at least $8$ out of $10$ answers on a true-false examination is:

• A. $\frac{7}{64}$
• B. $\frac{7}{128}$
• C. $\frac{45}{1024}$
• D. $\frac{175}{1024}$

Answer 1

The correct option is B $\frac{7}{128}$

The probability of guessing True or False question correct is $\frac{1}{2}$ and the probability of guessing wrong is $\frac{1}{2}$.

The probability of guessing atleast $8$ questions correct out of $10$ is ${}^{10}{C}_8{\left(\frac{1}{2}\right)}^{10}+{}^{10}{C}_9{\left(\frac{1}{2}\right)}^{10}+{}^{10}{C}_{10}{\left(\frac{1}{2}\right)}^{10}=\frac{7}{128}$

Therefore the correct option is $B$.