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# Probability

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James Choi, David Laibson, and Brigitte Madrian conducted an experiment to study the choices made in fund selection. Suppose 100 undergraduate students and 100 MBA students were selected. When presented with four S&P 500 index funds that were identical except for their fees, undergraduate and MBA students chose the funds as follows

Student Group
Lowest Cost Fund 19 19
Second Lowest Cost Fund 37 40
Third Lowest Cost Fund 17 23
Highest Cost Fund 27 18

If a student is selected at random, what is the probablitiy that he or she

a. Selected the lowest or second lowest cost fund?
b. Selected the lowest cost fund and is an undergraduate
c. Selected the lowest cost fund or is an undergraduate
d. Given that a student is an undergraduate, what is the probability that he or she selected the highest cost fund
e. Do you think undergraduate students and graduate students differ in their fund selection?