What are the chances?

這是國外某大科技公司的面試題. 目的是考你的推理思維, 錯對反而不是重點.

difficult to estimate.

反正無人會試解...

我把數學家　John Allen Paulos　的想法說出來吧!

.....assuming　that after more than two thousand years the exhaled molecules are uniformly spread about the world and the vast majority are still free in the atmosphere. Given these reasonably valid assumptions, the problem of determining the relevant probability is straightforward. If there are N molecules of air in the world and Caesar exhaled A of them, then the probability that any given molecule you inhale is from Caesar is A/N. The probability that any given molecule you inhale is not from Caesar is thus 1 - A/N. By the multiplication principle, if you inhale three molecules, the probability that none of these three is from Caesar is [1 - A/N]3. Similarly, if you inhale B molecules, the probability that none of them is from Caesar is approximately [1 - A/N]B. Hence, the probability of the complementary event, of your inhaling at least one of his exhaled molecules, is 1 - [1 - A/N]B. A, B (each about l/30th of a liter, or 2.2 X 1022), and N (about 1044 molecules)are such that this probability is more than 99%

超過99%？

/ or 2.2 X 1022), and N (about 1044 molecules)are such that this probability is more than 99%/

not reasonable.