Linus Pauling's Argument

On the occasion of his receiving second Nobel prize, Dr. Linus Pauling, the chemist, remarked that, while the chances of any person in the world receiving his first Nobel prize were one in several billion (the population of the world), the chances of receiving the second Nobel prize were one in several hundred (the total number of living people who had received the prize in the past) and that therefore it was less remarkable to receive one's second prize than one's first.

Solution

The chance of receiving a second Nobel prize only depends on the total number of living Nobel - prize winners if you know for a fact that the Nobel prize committee have decided to honor, again, one of the selected group. But Nobel prizes are awarded quite independently of past awards, and so the actual chance of being awarded two Nobel prizes is one chance in a billion times billion (if you suppose, which is implausible, that every human being on earth has an equal chance of an award).