Probability - using combinations (C) of 8 equal candidates for a job, 3 are qualified accountants, 4 are graduates and 2 have neither of these qualifications. Find: a) the probability a graduate get a job b) given that the qualified accountant has got the job, the probability that he's a graduate c) the probability that a qualified accountant gets a job, given that a graduate did not get a job.

We start by adding $3+4+2= 9$ but there are only 8 candidates so exactly one of of them must be both a graduate and a qualified accountant.

Now we have to explicitly assume that the qualifications have no bearing on the decision so that the winning candidate is chosen at random and there is only one position available.

Now

a) There are 4 graduates in 8 candidates so $P = \frac{4}{8} = \frac{1}{2}$

b) There are 3 accountants only one of them is a graduate so $P = \frac{1}{3}$

c) If we remove the graduates then we are left with 2 accountants and 2 unqualified so $P = \frac{2}{4} = \frac{1}{2}$