Assume that a certain virus can only spread by contact and has a 30% chance of s

Question

Assume that a certain virus can only spread by contact and has a 30% chance of spreading by handshake. Assume Eustace Clarence is infected and shakes hands with 3 other people. You can assume that infections are independent events. (In parts A,B,C,D,E: Assume all infections come from Eustace Clarence) Part A) What is the probability that ALL three of the people become infected? Part B) What is the probability that NONE of the three people become infected? Part C) Given that / Conditional on the first person being infected, what is the probability that both the second and the third person are infected. Part D) What is the probability that EXACTLY one of the three people becomes infected. Part E) What is the chance that the first OR the second person become infected. Part F) If we also account for other sources of infection in addition to Eustace Clarence, do your answer from parts A and B increase, decrease, or stay the same? Why?

Explanation / Answer

a)  probability that ALL three of the people become infected =(0.3)3 =0.027

b)  probability that NONE of the three people become infected =(1-0.3)3 =0.343

c)

being independent

P(2nd and 3rd infected|first infected) =P(second and third infected) =0.3*0.3 =0.09

d)probability that EXACTLY one of the three people becomes infected =3C1 (0.3)1(0.7)2 =0.441

e)

chance that the first OR the second person become infected =1-P( none of them infected) =1-(1-0.3)*(1-0.3)=0.51

f)

part A probability will increase as probability of having infection is increased due to addition of other factors.

part B probability will decrease as probability of not having infection is decreased.

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