Multiple choice

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

  1. ${ \left( \cfrac { 1 }{ 5 } \right) }^{ 6 }\\ \\ $
  2. ${ \left( \cfrac { 4 }{ 5 } \right) }^{ 6 }\\ \\ $
  3. $_{ 1 }^{ 6 }{ C }{ \left( \cfrac { 1 }{ 5 } \right) }^{ 5 }{ \left( \cfrac { 4 }{ 5 } \right) }^{ 1 }\\ \\ $
  4. $_{ 1 }^{ 6 }{ C }{ \left( \cfrac { 1 }{ 5 } \right) }^{ 1 }{ \left( \cfrac { 4 }{ 5 } \right) }^{ 5 }\\ \\ $
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B Correct answer
Explanation

This is a binomial distribution problem where n=6, p=0.2 (chance of disease), and q=0.8 (chance of no disease). The probability that no worker suffers from the disease is q^6 = (0.8)^6 = (4/5)^6.

AI explanation

Using the binomial distribution formula, the probability of zero workers suffering from the disease out of six is calculated when the probability of success (having the disease) is 1/5. The probability of a worker not suffering from the disease is 1 - 1/5 = 4/5. The probability of all 6 workers not suffering from the disease is (4/5) multiplied by itself 6 times, which equals (4/5)^6. The result is (4/5)^6.

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