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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 no one out of 6 workers suffers from a disease?

Options

  1. A665729\frac{665}{729}
  2. B64729\frac{64}{729}
  3. C4243\frac{4}{243}
  4. D1729\frac{1}{729}

Correct answer

B. 64729\frac{64}{729}

Step-by-step solution

Let P=\mathrm{P}= probability of workers which in suffering from disease. =13∴q=1−13=23P(X=0)=6C0(13)0(23)6=2636=64729=\frac{1}{3}\therefore \mathrm{q}=1-\frac{1}{3}=\frac{2}{3}P(X=0)=6_{C_0}\left(\frac{1}{3}\right)^0\left(\frac{2}{3}\right)^6=\frac{2^6}{3^6}=\frac{64}{729}
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