Assume that a certain virus can only spread by contact and has a 40% chance of s

Question

Assume that a certain virus can only spread by contact and has a 40% 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.

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) 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.

Explanation / Answer

Ans:

a) proabity that all are infected=0.4*0.4*0.4=0.064

b) probability that none is infected= 0.6*0.6*0.6=0.216

d)probablty that exactly one of the three=3*0.4*0.6*0.6=0.432

e)P(first or second person infected)=0.4*0.6*0.6+0.6*0.4*0.6=0.288

f)P(second or third infected/first infected)=P(first infected and third infected and first infected)/P(first infected)

=P(first infected)*P(second infected)*P(third infected)/P(thied infected)

=P(second infected)*P( third infected)

=0.4*0.4=0.16

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