Enigma 1747: Mind your Ps and Qs
From New Scientist #2915, 4th May 2013 [link]
I applied for a job and had two interviews. The two interviewers had to decide independently whether or not I was suitable. Only after both interviews were the two decisions announced and the approval of both was needed to get the job. Apparently the first interviewer approved one in every P applicants (where P is a whole number) and decided that the rest were unsuitable. Then, for any of the first interviewer’s decisions, there was only a one in Q chance that the second interviewer agreed with the first (where Q is a larger integer). After the second interview, the interviewer told me that he had approved my application. However, he warned me not to get too excited because there was only a one in P+Q chance that I had got the job.
What are the values of P and Q?