Problem 4 (8 points). Five hundred and fifty college seniors attending a career
ID: 3370724 • Letter: P
Question
Problem 4 (8 points). Five hundred and fifty college seniors attending a career fair at a university were categorized according to gender and according to primary career motivation, as summarized in the following table. Primary Career Motivation Money Allowed to Be Creative Sense of Giving to Society Total Male 82 Female 68 123 93 216 101 83 184 306 244 550 Total If one of these students is to be selected at random, find the probability that the student selected will satisfy each condition. (a) The student is male. (b) The student is a female or motivated primarily by creativity. (c) The student is female, given that their primary motivation is not money ) The student is motivated by money or a sense of giving back to society, given that the student is male. Problem 5 (5 points; Extra Credit). Show that if E and F are independent events, then P(EnF) P(E) P(F).Explanation / Answer
Males = 306
females =244
total students =550
a)
P(male) = (number of males)/total students = 306/550 =153/275
b)
P(female or motivated primarily by creativity) = P(female) +P(motivated primarily by creativity) -P(female and movtivated primarily by creativity)
= (244+216-93)/550
=367/550
c)
We are given that their primary motivation is not money
so we have to focus only on second and third column
total is 216+184 =400
From this sample space,number of females are 93+83 =176
so P(female | student's motivation is not money) = 176/400 =11/25
d)
we are given that student is male
so we have to focus only on the first row which is of male
so total male students are 306
out of these ,students which are motivated by either money or sense of giving to society = 82+101 =183
so probability = 183/306
= 61/102
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