The probability of success of a given vaccine is 0.82, that is, if a vaccinated patient...

The probability of success of a given vaccine is 0.82, that is, if a vaccinated patient is exposed to the disease, the probability of getting it is 18%. If I select 15 vaccinated patients, calculate the probability that:

a) None suffer the disease (3 pts)

b) Everyone suffers the disease (5 pts)

c) Two of them contract the disease (5 pts)

d) Determine the expected number of patients who will contract the disease (2 pts)

e) To complete a clinical study, 14 vaccinated patients who contract the disease are needed. What is the expected number of vaccinated patients who must be exposed to the disease to achieve the 14 required? (5 pts)

f) If of the 15, it is known that at least 2 contracted the disease, what is the probability that less than 6 of the 15 vaccinated will contract the disease?

Expert Solution

We use the formula of the p.m.f of binomial random variable mentioned above as this follows a binomial distribution and calculate the required probabilities.

orchestra answered 1 year ago

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