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Home  >>  CBSE XII  >>  Math  >>  Probability
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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} $

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1 Answer

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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

 

answered Feb 19, 2013 by poojasapani_1
edited Mar 14, 2013 by poojasapani_1
 

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