d. Comment on the differences in the probabilities computed in parts (b) and ()

Question

d. Comment on the differences in the probabilities computed in parts (b) and () 44, According to the Open Doors 2011 Report, 9.5% of all full-time U.S. undergraduate students studied abroad during the 2009-2010 academic year (Institute of International Education, November 14, 2011)Assume that participation records show women make up 60% of the students who studied abroad during the 2009-2010 academic year, but women make up only 49% of the students who didn't participate Let Al = the student studied abroad during the 2009-2010 academic year A2 the student did not study abroad during the 2009-2010 academic year the student is a female student Using the given information, what are the values for P(A). PiA).PWA), and b. What is the probability that a female student studied abroad during the 2009-2010 c. What is the probability that a male student studied abroad during the 2009-2010 d. Given the preceding results, what were the percentage of women and the percentage academic year? academic year? of men studying full-time during the 2009-2010 academic year? 5) (10 points) #44 Page 205 The events associated with this problem are A, = studied abroad A2 = DID NOT study abroad w = female student M = male student (A) = 0.095 P(h) = 0.905 P(WIAJ 0.60 P(W1A2) 0.49 According to Bayes' Theorem, given that a student is a woman, the probability she studied abroad is P(WIA)P(A1) Calculate this probability

Explanation / Answer

Sure, I think you want an answer to the Q5. Here' how to solve the problem:

5)

P(A1|W) = P(W|A1)*P(A1)/ (P(W|A1)*P(A1)+P(W|A2)*P(A2)

=(.60*.095)/(.60*.095+.49*.905)

=0.1139

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