Question

What is the probability of getting $80\%$ or more of the questions correct on a $10$-question true-false exam merely by guessing?

• A. $\frac{1}{16}$
• B. $\frac{5}{32}$
• C. $\frac{3}{16}$
• D. $\frac{7}{32}$
• E. $\frac{7}{128}$

Answer 1

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

The probability of guessing true is equal to probability of guessing false is $\frac{1}{2}$.
Therefore probability of getting $8$ or more questions right among $10$ questions is ${}^{10}{C}_8{\left(\frac{1}{2}\right)}^{10}{+}^{10}{C}_9{\left(\frac{1}{2}\right)}^{10}{+}^{10}{C}_{10}{\left(\frac{1}{2}\right)}^{10}=\frac{56}{2^{10}}=\frac{7}{128}$