gugliandalf wrote:
Let's say you just threw 5 Tails, your chance for a Head keeps being 50%. Right?
Right!
But what if you consider next throw as #6 in the serie? Your chance of SIX tails is 1.5% (5 Tails have 3.1%), that would make a Head 98.5% likely. Much depends on the way you look at it... 
Not exactly.
The key phrase is "statistic has no memory" (except for the great numbers law, but that is only for great number series, and this is not the proper case)
You have to calculate probability on the whole event you are going to predict (ie: not already happened).
If you say: "I'm going to get six tails on a row", then you can calculate your chances as 1.5625%.
But if after 5 throws you calculate again the probability for the next throw, it will be 50%.
This is easy to understand: the complete probability of a serie prediction can be calculated as:
(1/PossibleResults)^NumberOfResultPredicted.
So if you try to predict 6 results in a row using a device with 2 possible results (a coin), the formula is (1/2)^6 = 0.015625 = 1.5625 % . But after you get the first correct result, your goal is only for the 5 remaining predicted results, so the new formula is (1/2)^5 = 0.03125 = 3.125%.
If you are lucky enought to get the first 5 results as predicted, the last throw formula will be this one: (1/2)^1 = 0,5 = 50%.
Anyway statistical predictions are not always easy to understand. There are several cases where the solution of a statistical problem is absolutely counterintuitive. A good example is the Monty Hall problem: http://en.wikipedia.org/wiki/Monty_Hall_problem
Bye
Fourth
Btw:
This may be by far the most off topics argument I ever touched in this forum  |
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