Question

Virus X is a new virus infecting people. Some people get

Answer 1

Solution :

P(disease | virus) = 0.5

P(no disease | virus) = 0.5

P(john has virus) = 50% = 0.5

P(john doesn't have virus) = 1 - 50% = 0.5

P(three people don't develop disease | john has virus)

= P(no disease | virus)*P(no disease | virus)*P(no disease | virus)

= 0.5*0.5*0.5

= 0.125

P(three people don't have disease | john doesn't have virus) = 1

{if john doesn't have virus then 3 persons that he touches havve no chance of disease}

P(three persons no disease) = P(three people don't develop disease | john has virus)*P(john has virus) + P(three people don't have disease | john doesn't have virus) *P(john doesn't have virus)

= 0.125*0.5 + 1*0.5

= 0.5625

P(john has virus | three persons no disease) = P(three people don't develop disease | john has virus)*P(john has virus) / P(three persons no disease)

= 0.125*0.5 / 0.5625

= 0.11

P(4th develops disease | three persons no disease)

= P(develops disease | virus) * P(john has virus | three persons no disease)

= 0.50 * 0.11

= 0.055

P(4th develops disease | three persons no disease) = 0.055

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