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In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded.What is the probability of not getting a prize if you buy two tickets

$\begin{array}{1 1}(A)\;\large\frac{9990C_2}{10000C_2}\\(B)\;\large\frac{9980C_2}{10000C_2}\\(C)\;\large\frac{9970C_2}{10,000C_2}\\(D)\;\large\frac{9000C_2}{10,000C_2}\end{array} $

1 Answer

  • $nC_r=\large\frac{n!}{r!(n-r)!}$
  • Required probability=$\large\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{n(E)}{n(S)}$
Step 1:
Given total tickets =10,000
Out of which 10 tickets have prizes 9990 are blank
Total number of outcomes =$10000C_2$
Number of ways in which 2 tickets are without prize =$9990C_2$
Step 2:
$\therefore$ Required probability =$\large\frac{9990C_2}{10000C_2}$
Hence (A) is the correct answer.
answered Jul 2, 2014 by sreemathi.v

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