Suppose that 20% of all individuals have an adverse reaction to a particular dru

Question

Suppose that 20% of all individuals have an adverse reaction to a particular drug. A medical researcher will administer the drug to one individual after another until the first adverse reaction occurs. Define an appropriate random variable and use its distribution to answer the following questions.

a. What is the probability that when the experiment terminates, four individuals have not had adverse reactions?
b. What is the probability that the drug is administered to exactly five individuals?
c. What is the probability that at most four individuals do not have an adverse reaction?

Explanation / Answer

X will be distributed slightly different than a negative binomial distribution since NB will also account for combinations like: ANNNN, NANNN, NNANN, and NNNAN (all of which are not possible under the experiment rules).
So simply P[X=5] = (.2)(.2)(.2)(.2)(.8) = .00128

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