Question 1092889: According to a recent report, 60% of U.S. college graduates cannot find a full time job in their chosen profession. Assume 64% of the college graduates who cannot find a job are female and that 39% of the college graduates who can find a job are female. Given a male college graduate, find the probability he cannot find a full time job in his chosen profession?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! set up a table that looks like this:
% can find a job % can't find a job % total
male 24.4 21.6 46.0
female 15.6 38.4 54.0
total 40.0 60.0 100.0
you start off with 60% of all students who can't find a job which means that 40% can.
you then are told that 64% of the students who can't find a job are female.
64% of 60% is equal to .64 * .60 = .385 * 100% = 38.4% of all students are females that can't find a job.
the balance have to be males, therefore 60% - 38.4% = 21.6% of all students are males that can't find a job.
you then are told that 39% of the students who can find a job are female.
39% of 40% is equal to .39 * .4 = .156 * 100% = 15.6% of all students are females that can find a job.
the balance have to be male, therefore 40% - 15.6% = 24.4% of all students are males that can find a job.
from the table, you can see that the total percent of males is 46% and the total percent of females is 54%.
you are asked to find the probability that a graduate cannot find a job given that he is a male.
the probability that he is a male is 46%.
the probability that he is a male and can't find a job is 21.6%.
21.6 / 46 = .4695652174
the probability that a college student can't find a job given that he is a male is .4695652174 which is equal to 46.96% rounded to 2 decimal places.
this might make more sense if you put it into numbers.
assume 1000 students in total
60% can't find a job.
40% can.
this means 600 can't find a job and 400 can.
64% of the ones who can't find a job are female.
this means that .64 * 600 = 384 female who can't find a job.
this means that 600 - 384 = 216 males who can't find a job.
39% of the one who can find a job are female.
this means that .39 * 400 = 156 females who can find a job.
this means that 400 - 156 = 244 males who can find a job.
add up the total females and you get 384 who can't find a job plus 156 who can for a total of 540 female graduates.
add up the total males and you get 216 who can't find a job and 244 who can for a total of 460 male graduates.
your table will look like this:
% can find a job % can't find a job % total
male 244 216 460
female 156 384 540
total 400 600 1000
you want to know the probability that a student can't find a job in his profession given that the student is a male.
216 male students can't find a job.
the number of male students is equal to 460.
the probability that a student can't find a job given that the student is a male is equal to 216 / 460 = .4695652174
the formula to use is:
probability that a student can't find a job given that the students is a male is equal to the probability that the student is a male and can't find a job divided by the probability that the student is a male.
in algebraic terms, this would be p(NJ given M) = p(NJ and M) / p(M)
p(M) is the probability that the student is a male.
p(NJ and M) is the probability that the student can't find a job and is a male.
from the first table, you can see that:
p(M) = 46%
p(NJ and M) = 21.6%
p(NJ given M) = p(NJ and M) / p(M) = 21.6% / 46% = .4695652174
that equivalent to 46.96% rounded to 2 decimal places.
from the second table you can see that the number of men out of a total 1000 students who can't find a job is 216 and that there are 460 men.
216/460 = .4695652174 which is equal to 46.96% rounded to 2 decimal places.
the number of students was chosen to be 1000 because the arithmetic was easier that way and there was a direct correlation to the percents.
any number of student could have been used and you would get the same percentages.
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