I am a moderate smoker. I find a pretty girl working in the same company, smokes sporadically in the same smoking room.

A casual thought came into my mind. Say, just like a mathematical puzzle. If both the girl and I have completely the same habit in smoking, for example, let it to be more mathematically: In eight hours of a working day, the girl totally smokes 6 cigarettes, each for 10 minutes, and only one cigarette for each time. Suppose she enters the smoking room at random timing absolutely. And all above is the same to me. Then what is the probability that I can meet the pretty girl at one time when I enter the smoking room?

In probability theory, if a kind of event happens sporadically during a period of time or in some particular space stochastically, we identify the happening of that kind of event as “Poisson distribution”, which is discrete.

On the other hand, the probability of the next Poissonian event happens in the following time is denoted by “Exponential distribution”.

Accordingly, in this story, the girl and I both have the same randomness, with no mutual interference. The probability of meeting the girl is exactly congruent to the probability of the next poissonian event happens in the following time .

,

Integrate it: