Question 1092889
set up a table that looks like this:


<pre>


               % 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

</pre>


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:


<pre>


               % can find a job         % can't find a job       % total

male                244                       216                  460

female              156                       384                  540

total               400                       600                 1000

</pre>


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.