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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Probability

NDA 2022 · Mathematics · Probability

The incidence of suffering from a disease among workers in an...

The incidence of suffering from a disease among workers in an industry has a chance of 3313%33 \frac{1}{3} \%. What is the probability that exactly 3 out of 6 workers suffer from a disease?

Options

  1. A80729\frac{80}{729}
  2. B1081\frac{10}{81}
  3. C10243\frac{10}{243}
  4. D160729\frac{160}{729}

Correct answer

D. 160729\frac{160}{729}

Step-by-step solution

Let P=\mathrm{P}= probability of workers which in suffering from disease. =13∴q=1−13=23P(x=3)=6C3(13)3(13)3=6.5.43.2.1×836=160729=\frac{1}{3}\therefore \mathrm{q}=1-\frac{1}{3}=\frac{2}{3}P(x=3)=6_{C_3}\left(\frac{1}{3}\right)^3\left(\frac{1}{3}\right)^3=\frac{6.5.4}{3.2.1} \times \frac{8}{3^6}=\frac{160}{729}
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