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# 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}  Can you answer this question? ## 1 Answer 0 votes 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