Probability of finding a job A candidate is selected for interview for 3 posts.The number of candidates for the first, second and third posts are 3,4 and 2 respectively. What is the probability of getting at least one post?
My Solution: 
P(Candidate gets first job) = 1/3
P(Candidate gets second job) = 1/4
P(Candidate gets 3rd job) = 1/2

P(Candidate gets at least one job) = 1/3 + 1/4 + 1/2 
                                   = (4 + 3 + 6)/12

This gives me a probability greater than 1. What seems to be wrong with my method?
 A: The probability the candidate does not get an offer from the first interview is $\frac{2}{3}$. The probability she doesn't get an offer from the second is $\frac{3}{4}$, and the probability she doesn't get an offer from the third is $\frac{1}{2}$.
So the probability she does not get an offer at all is $\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{1}{2}=\frac{1}{4}$. Here we are assuming (unrealistically) independence.
Thus the probability she gets at least one offer is $\frac{3}{4}$.
The thing that is wrong about your method is that you are double-counting the cases where she gets $2$ offers, and triple-counting the cases where she gets $3$ offers. That is why your sum is greater than the correct value. Luckily, it turned out to be grater than $1$, which makes it clear that something is not right.
Later, you will learn how to get rid of such multiple counting by using the Method of Inclusion/Exclusion. However, I am guessing you are not yet at that point in the course, so took the simpler approach above.
Remark: We made the totally unreasonable assumption that job offers are given at random, that if there are $3$ people interviewed, exactly one, chosen at random, will get an offer. That's not quite the way the world works! 
A: you need to figure out the P(A or B or C) which is P(A) + P(B) + P(C) - P(A and B and C) - P(A and B) - P(A and C) - P(B and C)
so would be 1/4 + 1/2 + 1/3 - [(1/4)(1/2)(1/3)] - [(1/4)(1/2)] - [(1/4)(1/3)] - [(1/2)(1/3)]
which is 
13/2 - 1/24 - 1/8 - 1/12 - 1/6
which comes to 3/4 just like the original poster said, but without showing the complicated math.  The way they did it was a lot easier to figure out, because you CAN get 0 jobs, but you won't be able to get all 3 jobs.  So using the multiplication rule of probabilities to figure out the P of getting 0 jobs and subtracting that from 1 gives you the probability of getting at least one job, which is all we care about.
