Suppose That Two Employees Have to Be Fired from a Group

Suppose that two employees have to be fired from a group of seven:
- Amy, female, age 35
- Bob, male, age 41
- Chad, male, age 43
- Diana, female, age 44
- Elvis, male, age 49
- Frank, male, age 61
- Ginger, female, age 62
Suppose for now that the company selects the two employees to be fired at random, so all possible pairs of people have the same probability of being fired.
a. List all outcomes in the sample space. In other words, list all possible pairs of people that can be chosen from this group of seven people. (To save time and space, just use initials. For example, write AB to represent the (Amy, Bob) pair.)
b. Determine the probability (both as a fraction and a decimal) that both employees selected are female.
c. Determine the probability (both as a fraction and a decimal) that the average age of the employees selected is older than 50.
d. Determine the probability that both employees selected are older than 60 .
Suppose that Frank and Ginger are the employees selected to be fired. They proceed to file a lawsuit, alleging that the company is guilty of age discrimination for choosing the two oldest employees to fire. The company responds that it did not discriminate; it simply happened to choose these two by random chance.
e. Does your probability analysis provide evidence to support the allegation of age discrimination? Explain (with 1-3 sentences) the reasoning process behind your answer.