Concept explainers
Second Paradox: The probability of a male applicant being admitted to a graduate school can be higher than the probability for a female applicant, even though for each department the probability of a female being admitted is higher. (This apparent contradiction is known as Simpson’s paradox.)
To simplify matters, consider a university with two professional graduate programs, medicine and law. Suppose that last year 1000 men and 1000 women applied, and the outcome was as shown in Table 1.
Table 1 |
||||||
Men |
Women |
|||||
Applied |
Accepted |
Rejected |
Applied |
Accepted |
Rejected |
|
Law Medicine |
700 300 |
560 40 |
140 260 |
400 600 |
340 160 |
60 440 |
What is the probability that a male applicant was accepted to a professional program? A female applicant?
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