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Questions  >>  CBSE XII  >>  Math  >>  Probability
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Q)

Suppose 10,000 tickets are sold in a lottery each for Re1.First prize is of Rs 3000 and the second prize is of Rs 2000.There are three third prizes of Rs 500 each.If you buy one ticket,what is your expectation.

$\begin{array}{1 1}(A)\;0.65\\(B)\;0.75\\(C)\;0.85\\(D)\;0.95\end{array} $

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A)
Toolbox:
  • 10,000 tickets
  • 1 ticket is bought
  • We define X=The expected value of money for each prize1 ,2 and 3
  • X=\((3000\,;2000\;,500)\)
  • \(p_i\)=probability of getting '2'prize
  • i=1,2,3
  • Expected proze money
  • =\(\Large\;\sum_{i=1}^{3} p_i x_i\)
P\(x=x_1\)=\(\Large\frac{1}{10,000}\)
P\(x=x_2\)=\(\Large\frac{1}{10,000}\)
P\(x=x_3\)=\(\Large\frac{3}{10,000}\)
\(E(X)=\Large\;3000\times\;\frac{1}{10,000}\;+2000\times\;\frac{1}{10,000}\;+500\times\;\frac{1}{10,000}\)
=\(\Large\frac{65}{100}\)
=\(0.65\)

 

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