Monday, November 21, 2016

low chance of happening

I have been reading about human evolution and the influence of genetics.   An individual gene might have a low chance of being part of someone's genetic makeup and yet still manage to be present.  How can a low probability event happen?

An easy answer is have a very large number of cases where it might happen.  You may have heard the statement "If something can happen, it will eventually"  You can see that in the case of a lottery involving many people, the chance that any given one of them wins the big prize is very small. Yet, someone will win.  

A good book on this subject is The Improbability Principle by David Hand.  The really large number of trials principle of producing one or more instances of the low probability event is easily understood in the case of the lottery.  

I suspect that when people try to think of a number that might stand for the probability of a rare or unlikely event, they hesitate to use a figure lower than 10%.  When we are dealing in percentages, 1 % can seem so small as to be nearly impossible.  Yet, in the case of many important events in our lives, 1% can be a very large probability.

Here is a link to the Wikipedia article on auto deaths in the US:

You can see that many events have much lower chance of happening than 1%.  Wisconsin has about 5 million people, 5,000,000.  1% of 5 million is 50,000 or just about twice the entire population of my town including the students at the local university.  Very few events will occur for everybody in town and everybody in another town of the same size.   Because numbers much smaller than 1 in 100 can be quite important, statisticians often use a larger number for a base than 100.  Many statistics related to health and accidents are based on the number of occurrences per 100,000 instead of 100.  The names of the numbers give us a clue: one hundred thousand = one hundred a thousand times.

I have read that people often feel in their gut that if something has a probability of 70%, they have a feeling that the event is sure to happen.  That would mean that a probability of 30% is low enough to be ignored.  But it is clear that if a 1% chance can actually be pretty large, 30% can be gigantic.

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