A poll was conducted by making random phone calls to people in the United States. 3000 people called agreed to participate in the survey. The participants were asked if they had received the influenza vaccine and if they had contracted the illness in the previous flu season.

The following information was found:
- Of those who had received the vaccine, 75 contracted the flu.
- Of those who did not receive the vaccine, 410 contracted the flu.
- Of the 3000 phone calls made, 860 had received the vaccine.

Questions

(1) First, change this information into proper notation to solve the problem.
(2) What type of probability is this example problem? How do you know?
(3) Set up a table to answer the questions below (This should look similar to the IE 424 Probability

Examples I, the example(s) regarding the microprocessors).
(4) The FDA would like to use the information to find:
- the probability of not getting the flu?
- the probability that a person did receive the vaccine and did not get the flu?
- the probability that a person did not receive the vaccine and did not get the flu?

(5) For their next flu vaccine marketing campaign, the Marketing Department of Aventis would like to calculate statistics regarding the following:
- the probability that a person did receive the vaccine?
- the probability that the person did not receive the vaccine and got the flu?

(6) Based on the information, the Quality Control Department and Product Improvement Team at Aventis would like to know:
- the probability that a person did receive the vaccine and still got the flu?