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# I can’t understand how probability makes sense

\$ \begingroup \$ You ask a natural skill, or physical, wonder. Mathemathics has nothing to do with bumping into atoms. not directly .
In the physical world, a coin can land and stay on the boundary. In probability, 50:50 is not 49.9999:49.9999:0.00002. ( Add two miles of nines and zeroes if you like, there is adequate )

If thus, then in a strictly random experiment would the resultant role be 50-50 ?

In the long run, yes. But it could even fluctuate, so it would be 50:50 overall, but still not random. You should do 10 times 20 tosses, and comparison. Or even 100 times 2 tosses to see the boring 4 HH, TT, HT and TH combinations : you get some double heads, some double tails, and same measure of mix. ( see added bottom part )
Do n’t polish your coin or toss it high, hoping for a 50:50 undertake – you only have a “ largely somewhere around 50:50 ” guarantee, and it contains “ by and large ” .
You know quite well what a “ long enough run ” is : after ten oder twenty events you get a good depression, and you will evening clearly note the remainder between a sequences like 0000011111 and 0010111010 .
You would have to plot each pass or dock over time, and then use some statistical tests to look for non-random distributions .
Something outside the “ confidence ” interval then needs re-evaluation, if you want to ne sure ( radius ) .
In the end, you can not know : say you toss a coin one hundred times and actually get 100:0 ! You repeat. normal, say 47:53 .
You may never find out, why you got 100:0 in one of the “ runs ”. The wind ? preferably not. You tossed correctly. A magnetic field ? Or was it truly coincidence ? Do you have witnesses ?
At least mathematics can tell you how identical improbable a 100:0 mint flip is, if ( and only if ) it was “ arrant ” random .
After you hear the probability, you would be very identical baffled. “ I tossed 100 times and got 100 heads. cipher even saw it. I did n’t even bet on it. ” fortunately, this never happens .
ever .
Or does it ?
( maybe it happens in catastrophies and miracles, but not in statistical experiments )
binding to 50-50, and pascal triangle. As a complete “ decision ” tree, a repeated ( or multi- ) coin flip can be written like this :
first toss/coin : 0 or 1 second base : 0, then ( 0 or 1 ) or 1, then ( 0 or 1 )

— > Two coins can only come in 4 different combinations : `00, 01, 10, 11`
Since “ 01 ” and “ 10 ” is the same ( order does not matter here ) you lump them in concert and get : one “ 00 ”, two “ mix ”, one “ 11 ” .
Or : two blend and two arrant .
— > with only two 50-50 events you have besides a 50-50 casual of getting 100:0 or 50:50 .
With three coins you reach the 1-3-3-1 line in pascal triangle :

``````00 and 1 or 0
01 and 1 or 0
10 and 1 or 0
11 and 1 or 0

000, 001;
010, 011; 100, 101
110, 111;
``````

now you have 8 combinations, and you see the design emergent :
“ 000 ” has precisely the same probabllity than say “ 100 ”, but : “ 100 ” has companions : “ 001 ”, “ 010 ”. These are the three with precisely one “ 1 ” :

``````no  "1": 000
one "1": 001, 010, 100
two "1": 011. 101. 110
all "1": 111
``````

2 out of 8 are saturated ( “ 000 ” and “ 111 ” ), 6 are blend ( but none can even be 50:50, only together do they contain 9 “ 1 ” and 9 “ 0 ” ) .
adjacent pascal triangle quarrel is 1-4-6-4-1. That will mean 6 out of 16 four-coin tosses will show precisely 2 heads and 2 tails. 8 out of 16 tosses will have some unequal mix of drumhead and tails, and 2 tosses will be strictly heads or strictly talis .
— > With 4 coins it is preferably improbable ( under 37 % ) to get a 50-50 result .
With 4000 coins it gets even more improbable to hit that single “ concentrate column ” precisely. Left and right to it, there are so many “ companions ”, that it is much more probable to get “ something like ” 50.103:49.897 than that single 50.000:50.00 column ,
If you find the pascal triangle unpractical for your 200 tosses, you might want to turn to gauss swerve ( “ distribution ” curl ) – but the core of this all ( “ discrepancy ” ) starts with pascal triangulum .

``````  x
xxx

xx
xx
xxxx

x
x
xxx
xxx
xxx
xxxxx
``````

If you want precisely Heads=Tails, then you better use precisely 2 coins : in about 50 % of tosses you will get precisely 50.0 % Heads. ( but “ failure ” will be a full 100 % or 0 % failure )

The more coins, the more probably it gets to come close to 50.0 %, but at the lapp prison term more unlikely to hit 50.0 % precisely. A 100 % or 0 % leave gets very improbable .
A kind of paradoxon of big numbers, but we all know :
“ it is not normal to be ( precisely ) normal ” .

source : https://leowiki.com
Category : Economy