The incidence of occupational disease in an industry is such that the workmen have a $10 \%$ chance of…

The incidence of occupational disease in an industry is such that the workmen have a $10 \%$ chance of suffering from it. The probability that out of 5 workmen, 3 or more will contract the disease is
  1. $0.0856$
  2. $0.000856$
  3. $0.00856$
  4. $0.0000856$

Solution

$\begin{aligned} & { }^5 C_3\left(\frac{1}{10}\right)^3 \cdot\left(\frac{9}{10}\right)^2+{ }^5 C_4\left(\frac{1}{10}\right)^4\left(\frac{9}{10}\right)^1+{ }^5 C_5\left(\frac{1}{10}\right)^5\left(\frac{9}{10}\right)^0 \\ & =10 \times \frac{81}{10^5}+5 \times \frac{9}{10^5}+1 \times \frac{1}{10^5} \\ & =\frac{810+45+1}{10^5}=\frac{856}{10^5}=0.00856\end{aligned}$

Asked in: MHT CET 2022 (06 Aug Shift 2)

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