Question

The incidence of occupational disease in an industry is such that the workers have a $20$% chance of suffering from it. The probability that out of 6 workers chosen at random, not even one will suffer from that disease is

• A. ${\left(\frac{1}{5}\right)}^6$
• B. ${\left(\frac{4}{5}\right)}^6$
• C. ${}_1^{6}C{\left(\frac{1}{5}\right)}^5{\left(\frac{4}{5}\right)}^1$
• D. ${}_1^{6}C{\left(\frac{1}{5}\right)}^1{\left(\frac{4}{5}\right)}^5$

Answer 1

The correct option is B ${\left(\frac{4}{5}\right)}^6$

Here $20$% of the workers have a chance of suffering from the disease.
Therefore
$p=\frac{20}{100}$
$=\frac{1}{5}$
$(1-p)=\frac{4}{5}$. ...(probability of not suffering from the disease).
Now the required probability, where out of 6, none suffers from the disease is
${}^6{C}_0(1-p{)}^6(p{)}^0$
$=(\frac{4}{5}{)}^6$