Today I wish to start a series of posts that are supposed to help my younger colleagues who will, in two months from now, compete for a position as INFN research scientists. 
The INFN has opened 73 new positions and the selection includes two written exams besides an evaluation of titles and an oral colloquium. The rules also say that the candidates will have to pass the written exams with a score of at least 140/200 on each, in order to access the oral colloquium. Of course, no information is given on how the tests will be graded, so 140 over 200 does not really mean much at this point.

Given the fact that the number of candidates is expected to be of the order of 500 to 1000, and that the works of the selection committee have to finish by the end of the year, it is easy to expect that the written tests will be tough to pass - it is unthinkable that the committee members may fancy the option of entertaining themselves with many hundreds of colloquia. 

If I were in the committee, I would indeed plan a first written test, with multiple choice questions or something similar easy to rate; this would allow me to filter the candidates very early on. I know this sounds bad, but it's a question of survival...

In the assumption that one of the written tests will be a set of physics questions, not dissimilar to the one I myself had to face 11 years ago when I participated in a similar selection, I thought I would publish here a few sample physics tests that could be similar to those that the candidates will have to face in two months. 

The questions I am thinking about are "simple" - they should take no more than 5 to 10 minutes to answer. But they should manage to test some specific knowledge of experimental particle physics, and allow the examiner to gauge the depth of the candidates' understanding of the matter.

The rules of the game are as follows: I post a question, you are free to give your answer in the comments thread, and then we discuss the answers. Ideally I would like to post a question every day... But I guess the rate will end up to be smaller; hence the title of this series of posts is more wishful thinking than anything else.

So here we go. Today's question is about a hadron collider.
A proton-proton collider with center-of-mass energy of a few TeV produces an instantaneous luminosity of 10^32 cm^-2 s^-1 in the interaction region, with a bunch-crossing rate of 500 nanoseconds. Estimate the probability that a bunch crossing produces more than one inelastic collision, and provide information on how you derive your answer.