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?
The probability the candidate does not get an offer from the first interview is 2/3. The probability she doesn’t get an offer from the second is 3/4, and the probability she doesn’t get an offer from the third is 1/2.
So the probability she does not get an offer at all is 2/3⋅/34⋅1/2=1/4. Here we are assuming (unrealistically) independence.
Thus the probability she gets at least one offer is 3/4.
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!