Question

The incidence of occupational disease in an industry is such that the workers have a $20$ percent chance of suffering from it. The probability that out of $6$ workers chosen at random, exactly four will suffer is

• A. ${}_4^{6}C{\left(\frac{2}{5}\right)}^2{\left(\frac{3}{5}\right)}^4$
• B. ${}_4^{6}C{\left(\frac{2}{5}\right)}^4{\left(\frac{3}{5}\right)}^2$
• C. ${}_4^{6}C{\left(\frac{4}{5}\right)}^2{\left(\frac{1}{5}\right)}^4$
• D. ${}_4^{6}C{\left(\frac{1}{5}\right)}^2{\left(\frac{4}{5}\right)}^4$

Answer 1

Answer: (C)

${}_4^{6}C{\left(\frac{4}{5}\right)}^2{\left(\frac{1}{5}\right)}^4$

Probability of suffering from occupational disease $=\frac{20}{100}=\frac{1}{5}$

Probability of not suffering from occupational disease $=1-\frac{1}{5}=\frac{4}{5}$

Selecting exactly four workers out of six those are suffering: ${}_4^{6}C$

Probability that out of 6 workers, exactly four will suffer:
${}_4^{6}C{\left(\frac{4}{5}\right)}^2{\left(\frac{1}{5}\right)}^4$