When One consider "String", it should be clear what is the Collection Size.
Problems with strings are , their collection is of virtually infinite size and there is no end, and any probabilities measure relying on assumption of finite collection size will not be correct.
Say with strings..in continuous tosses,
......H H H T T H H H H H T H T H H T T T H H H .......
1) I saw the Strings in Red color and yea, they are with Teal color also.
2) Opps, i saw two Black H before 3 Red H...yea its another H H H H H string
3 Teal H have 3 Black T prior to that....its another string....
there would be no end, and new strings can be obvious by unlimited combination. Why limit , to think 10 winning bets continuous is a string , before that 2 loosing bet might also make combination of 12 bet string....
Now saying probability of getting 3 H or 4 H...one is confining the collection size to limited numbers and that make sense to probabilities in that finite collection.
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Thanks for pointing this out. Of course, if you talk about a probability, you first need to specify the design of the experiment - or the rules of the game that you want to play.
With the toin cosses I assumed that you play one game as long as there is no heads. With this defintion every becomes a series of N tosses of tails and 1 heads, where the heads finishes the game.
Potential outcomes with a regular coin are
- H (no tail) -> probability 50%
- TH (one tail) -> probability 25%
- TTH (two tails) -> probability 12.5%
This definition of the game does not require a finite collection.
If you play a continuous tossing game and you look at the probability that the series of the last N tosses all resulted in tails X X X X X T T T , where X means anything (could be either T or H), then the probabilities of two consecutive events are dependent.
If you had a string of 3 Tails on event no. 1235, this conditions event no. 1236, as the chances to get another 3 tails in a row are now enhanced, if you know that the preceding 2 tosses resulted in tails. This is a conditional probability, and can be calculated by using the formula of Bayes.
Last edited by Fat Tails; January 11th, 2012 at 12:38 PM.
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Thanx for example, i had enjoyed these in my schooling.
When we set rule "as long as"...it make collection itself infinite.
We can get each new string with decreasing probabilities as pointed out by 3 first strings.
If i remember correctly Beyes Theorem is also on Finite Collection size...
See, this is how, your game will compares with Infinite Cells of resistances...removing any number of cells doesn't changes the net resistance between points A and B.
What it simulates in given toss example....if one remove diagonally Ts...it will still have "Fresh Start".....
nothing will change...and what string of sequence has gone cant be used in Conditional Probability calculation of getting H...cause Collection is non-ending.
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