Question 1122645: According to a recent report, 60% of U.S. college graduates cannot find a full time job in their chosen profession. Assume 57% of the college graduates who cannot find a job are female and that 26% of the college graduates who can find a job are female. (See exercise 58 on page 215 of your textbook for a similar problem.)
Given a male college graduate, find the probability he can find a full time job in his chosen profession.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 60% of all college graduates cannot find a job in their profession.
that means that 40% can.
26% of all college graduates who can find a job are women.
that means that 74% of all college graduates who can find a job are men.
you are also given that 57% of the college graduates who cannot find a job are men.
that means that 43% of the college graduates who cannot find a job are men.
consider that 60% of all college graduates can't find a job and that 43% of them are men.
that means that .43 * 60% = 25.8% of all college graduates who cannot find a job are men.
consider that 40% of all college graduates can find a job and that 74% of them are men.
that means that .74 * 40% = 29.6% of all college graduates who can find a job are men.
you have 25.8% of all college graduates who cannot find a job are men and you have 29.6% of all college graduates who can find a job are men.
that means that 29.6% + 25.8% = 55.4% of all college graduates are men.
of the college graduates who are men, 29.6% / 55.4% = 53.42960289% of them can find a job after graduation.
i believe that answers the question.
you could build a table as shown below:
male female total
can find a job 29.6% 10.5% 40%
cannot find a job 25.8% 34.2% 60%
total 55.4% 44.6% 100%
the table is populated as follows:
60% of all college graduates can't find a job.
that means 40% can.
26% of all college graduates who can find a job are female.
.26 * 40 = 10.4% of all college graduates who can find a job are female.
26% of all college graduates who can find a job are female means that 74% of all college graduates who can find a job are male.
.74 * 40 = 29.6% of all college graduates who can find a job are male.
57% of all college graduates who can't find a job are female.
.57 * 60 = 34.2% of all college graduates who can't find a job are female.
57% of all college graduates who can't find a job are female means that 43% of all college graduates who can't find a job are male.
.43 * 60 = 25.8% of all college graduates who can't find a job are men.
add up the columns to get 55.4% males and 44.6% females.
add up the rows to get 40% can't find a job and 60% can find a job.
that completes the table.
to see if this makes sense, assume there are 1000 college graduates.
40% can find a job and 60% can't.
that makes 400 who can and 600 who can't.
of the ones who can, 26% are female.
that makes 104 females 296 males who can find a job.
of the ones who can't, 57% are female.
that makes 342 females and 258 males who can't find a job.
the total number of males is 296 + 258 = 554.
out of those, 296 can find a job.
the percentage of males who can find a job is 296 / 554 = 53.42960289%.
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