In a major midwestern university, 55 percent of all undergraduates are female, 25 percent of all undergraduates belong to a Greek organization (fraternity or sorority), and 40 percent of all males belong to a Greek organization. What is the probability that one randomly selected undergraduate will be either a female or belong to a Greek organization?
A) .73
B) .55
C) .80
D) .07
E) .87

Question

Quizplus · Accepted Answer

To complete the contingency table and answer the question on the intersection of female or Greek, since the initial information includes a conditional statement, you need to calculate the intersection of male and Greek:
If P(Greek │ Male) = 40%. And 40% of .45 = .18. Then, Female & Greek = .25 − .18 = .07, or 7%. P(Female) = 55%. P(Greek) = 25%.
P(G ∪ F) = .55 + .25 − .07 = .73
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In a Major Midwestern University, 55 Percent of All Undergraduates