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Home  >>  CBSE XII  >>  Math  >>  Probability
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Ten coins are tossed.What is the probability of getting at least 8 heads?

$\begin{array}{1 1}(A)\;\large\frac{7}{128}\\(B)\;\large\frac{8}{122}\\(C)\;\large\frac{128}{7}\\(D)\;\large\frac{5}{128}\end{array} $

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1 Answer

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Toolbox:
  • In a toos of coin getting head and Tail are equally likely
  • P=P(H)=\(\large\frac{1}{2}\)
  • q=1-P=1-\(\large\frac{1}{2}\)=\(\large\frac{1}{2}\)
  • Tossed 10 times
  • N=10
  • X=\((0\;,1\;,2\;,3\;,4\;,5\;,6\;,7\;,8\;,9\;,10)\)
  • P(X=r)=\(\large\;C^n_r \;P^r\; Q^{n-r}\)
P(at least 8 heads )=P(X=8)=P(X=9)+p(X=10)
\(C^{10}_8\;\Large(\frac{1}{2}\;)^8\;(\frac{1}{2}\;)^{10}+C^{10}_9\;(\frac{1}{2}\;)^9\;(\frac{1}{2}\;)^1+\;C^{10}_{10}(\frac{1}{2}\;)^{10}\;(\frac{1}{2}\;)^0\)
=(\(\Large\frac{1}{2}\))\(^{10}\times\)[45+10+1]
=(\(\frac{1}{2}\))\(^{10}\times\)56
=\(\frac{7}{128}\)

 

answered Feb 27, 2013 by poojasapani_1
edited Jun 4, 2013 by poojasapani_1
 

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