Understanding the Probability of Coincidences: A Mathematical Perspective

[musicgold]

Hi,

I am reading a book that explains the mathematics behind coincidences experienced in our daily lives. In one example, the author derives that the chance that you will at least once experience one of a set of 100 rare events (each with a one-in-million chance of occurring on any day) in a period of 20 years is as high as 52%. I understand this part completely.

What stumps me is the author’s following comment: It means that for every 20 people you know, there is a greater than 50% chance that one of them will have an amazing story to tell during the course of a year.

My questions are:
1. Is the author using the 1 of 20 phrase, to indicate a 95% confidence interval (19 out of 20 times)?

2. How the author expects one of a group of 20 to experience a coincidence in a year’s time?

Thanks,

MG.

 

[HallsofIvy]

1. No. This has nothing to do with "confidence intervals".

2. You say you understand the probability of such an experience for one person, in 20 years is 0.52. All the second part is saying is that since "years" are independent (you are no more likely to have such an experience in one year than another) and "people" are independent (one person is nor more likely to have such an experience that another person), it doesn't matter whether you distribute over "years" or "persons". The probability that at least one person out of 20 will have such an experience in a given years is the same as that a given person will have at least one such an experience over 20 years: 0.52 or "a greater than 50% chance".

 

[musicgold]

HallsofIvy,

Thanks a lot. Great explanation !