Merck & Co. conducted a study to test the promise of its experimental AIDS vaccine ( The Boston Globe , September 22, 2007). Volunteers in the study were all free of the human immunodeficiency virus (HIV), which causes AIDS, at the start of the study, but all were at high risk for getting the virus. Volunteers were given either the vaccine or a dummy shot; 24 of 741 volunteers who got the vaccine became infected with HIV, whereas 21 of 762 volunteers who got the dummy shot became infected with HIV. The following table summarizes the results of the study.

a. Convert the contingency table into a joint probability table.
b. What is the probability that a randomly selected volunteer got vaccinated?
c. What is the probability that a randomly selected volunteer became infected with the HIV virus?
d. If the randomly selected volunteer was vaccinated, what is the probability that he/she got infected?
e. Are the events “Vaccinated” and “Infected” independent? Explain using probabilities. Given your answer, is it surprising that Merck & Co. ended enrollment and vaccination of volunteers in the study?Explain.

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