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Suppose that the fraction of infected people in a city is p = 0.01. 100 people...

Suppose that the fraction of infected people in a city is p = 0.01. 100 people from the city board a small cruise. You can assume that the people are unrelated to each other and randomly chosen so that each person is infected independently with probability p. You can also ignore the possibility that they infect each other while boarding.

Suppose that the virus test gives negative when the person has the virus with probability 0.2, and gives negative when the person does not have the virus with probability 0.95

  1. Find the probability that no one in the cruise has the virus.

  2. Find the probability that at most 2 people in the cruise has the virus.

  3. Find the probability that a person doesn’t have the virus if they test negative.

  4. Suppose that all the 100 persons are tested and all the tests come back negative. Find the probability that no one has the virus.

  5. Find the probability that no one has the virus given that one passenger tested positive.

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