Question

What is the probability of guessing correctly at least 8 out of 10 answers on a true -false examination?

• A. $\frac{11}{128}$
• B. $\frac{5}{128}$
• C. $\frac{13}{128}$
• D. $\frac{7}{128}$

Answer 1

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

$p(X\ge 8){=}_8^{10}\text{C}(\frac{1}{2}{)}^8(\frac{1}{2}{)}^2{+}_9^{10}\text{C}(\frac{1}{2}{)}^9(\frac{1}{2}{)}^1{+}_{10}^{10}\text{C}{(\frac{1}{2})}^{\left(10\right)}$$={(\frac{1}{2})}^{\left(10\right)}{[}_2^{10}\text{C}{+}_1^{10}\text{C}{+}_0^{10}\text{C}]$

$={(\frac{1}{2})}^{10}[45+10+1]$=$\frac{56}{8\times 2^7}$$=\frac{7}{128}$