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?
d. How many individuals would you expect to not have an adverse reaction, and to how many individuals would you expect the drug to be given?
e. What is the probability that the number of individuals given the drug is within 1 standard deviation of what you expect?