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

\$\begin{array}{1 1} (A)\;\large\frac{7}{64}\$$B)\;\large\frac{7}{128}\\(C)\;\large\frac{45}{1024}\\(D)\;\large\frac{7}{41}\end{array}  ## 1 Answer Toolbox: • In true or false question • p=p(getting correct answer)=\(\frac{1}{2}$$
• q=1-$$\frac{1}{2}$$=$$\frac{1}{2}$$
• $$p(x=r)-c^n_r\;p_r\;q_{n-r}\;n=10$$
p(x>8)=p(getting 8 or more question correct)
$$\large\;p(x=9)+p(x=9)+p(x=10)\;\;\;c^{10}_8(;\frac{1}{2})^8(\frac{1}{2})^2+c^{10}_9(\frac{1}{2})^9(\frac{1}{2})^1+c^{10}_{10}(\frac{1}{2})^0(\frac{1}{2})^{10}$$
$$\Large\frac{1}{28} [45+10+1]=\frac{56}{28}$$
$$\Large\frac{7}{128}$$
B -option is correct

edited Mar 14, 2013