Is probability logical?

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Reply Tue 3 Nov, 2009 10:26 pm
I understand how simple probability situations function but logically, it doesn't make sense.

Scenario: A coin is tossed and there is a 50% of it landing on heads and a 50% chance that it will land on tails. The probability of getting heads/tails twice in a row is 25% (.5 x .5). This 25% probability refers to the situation as a whole (not to any particular toss in the sequence).

So, a coin is tossed and lands on heads. The next toss is either 50% heads or 50% tails. To overall probability of the situation says that tails is then more likely an outcome, because that would satisfy the higher probability (h+t = 50%, h+h = 25%, t+t = 25%) which would of course be more likely. So after the first toss results in heads, the second tossed is supposedly more likely to be tails when you look at the overall situation regardless of the probability of the 2nd toss alone is half and half... According to probability, the first toss and the probability of the 2 tosses combines determines a different probability for the second toss other than the 1/2 and 1/2 probability of heads and tails.

I know i'm missing something, why is this?
 
Fido
 
Reply Tue 3 Nov, 2009 10:46 pm
@Yogi DMT,
There is a 99.999 percent chance that the coin will land... Probability is logical because when you know the probabilities you know what will happen, and what will happen, effect following cause, you know what is going to happen...
 
prothero
 
Reply Wed 4 Nov, 2009 01:52 am
@Yogi DMT,
Yogi DMT;101674 wrote:
I know i'm missing something, why is this?


Once you know the outcome of the first toss. The probablity of the second toss is .5 heads and .5 tails as it is for any indiviudal toss.

It is only in sequences of events (3,4,5 or more tosses) where the outcome of no event has yet been determined that the stochastic probabilities patterns can be applied.

Your quandry is a common misunderstanding.

If the first toss is already known to be heads, then the probability of two heads is now 50% not 25% like it was before the first toss occurred.
 
kennethamy
 
Reply Wed 4 Nov, 2009 06:57 am
@Yogi DMT,
Yogi DMT;101674 wrote:
I understand how simple probability situations function but logically, it doesn't make sense.

Scenario: A coin is tossed and there is a 50% of it landing on heads and a 50% chance that it will land on tails. The probability of getting heads/tails twice in a row is 25% (.5 x .5). This 25% probability refers to the situation as a whole (not to any particular toss in the sequence).

So, a coin is tossed and lands on heads. The next toss is either 50% heads or 50% tails. To overall probability of the situation says that tails is then more likely an outcome, because that would satisfy the higher probability (h+t = 50%, h+h = 25%, t+t = 25%) which would of course be more likely. So after the first toss results in heads, the second tossed is supposedly more likely to be tails when you look at the overall situation regardless of the probability of the 2nd toss alone is half and half... According to probability, the first toss and the probability of the 2 tosses combines determines a different probability for the second toss other than the 1/2 and 1/2 probability of heads and tails.

I know i'm missing something, why is this?


Yes, you are missing something. You are committing the notorious Gambler's fallacy.

Gambler's fallacy - Wikipedia, the free encyclopedia
 
Emil
 
Reply Wed 4 Nov, 2009 08:21 am
@Yogi DMT,
Yogi DMT;101674 wrote:
I understand how simple probability situations function but logically, it doesn't make sense.

Scenario: A coin is tossed and there is a 50% of it landing on heads and a 50% chance that it will land on tails. The probability of getting heads/tails twice in a row is 25% (.5 x .5). This 25% probability refers to the situation as a whole (not to any particular toss in the sequence).

So, a coin is tossed and lands on heads. The next toss is either 50% heads or 50% tails. To overall probability of the situation says that tails is then more likely an outcome, because that would satisfy the higher probability (h+t = 50%, h+h = 25%, t+t = 25%) which would of course be more likely. So after the first toss results in heads, the second tossed is supposedly more likely to be tails when you look at the overall situation regardless of the probability of the 2nd toss alone is half and half... According to probability, the first toss and the probability of the 2 tosses combines determines a different probability for the second toss other than the 1/2 and 1/2 probability of heads and tails.

I know i'm missing something, why is this?


The probability of the second coin does not change. Indeed you're flirting with the Gambler's Fallacy.
 
kennethamy
 
Reply Wed 4 Nov, 2009 08:49 am
@Emil,
Emil;101730 wrote:
The probability of the second coin does not change. Indeed you're flirting with the Gambler's Fallacy.


It's not flirting. It is a marriage.
 
Yogi DMT
 
Reply Wed 4 Nov, 2009 02:49 pm
@kennethamy,
kennethamy;101703 wrote:
Yes, you are missing something. You are committing the notorious Gambler's fallacy.

Gambler's fallacy - Wikipedia, the free encyclopedia


Basically haha, makes more sense now. Thanks
 
Kroni
 
Reply Wed 2 Dec, 2009 05:40 pm
@kennethamy,
Everyone is right, the odds change once the sequence of occurrences before it have been given.

Probability is a strange concept, though. On the surface it is very logical, but many times in the real world things don't play out the way the odds say they should. If you have pocket aces and someone else has pocket 2s, the 2s can still win if they hit 3 of a kind. What is the driving force that determines whether or not an event will follow the odds?
 
kennethamy
 
Reply Wed 2 Dec, 2009 07:44 pm
@Kroni,
Kroni;107664 wrote:
Everyone is right, the odds change once the sequence of occurrences before it have been given.

Probability is a strange concept, though. On the surface it is very logical, but many times in the real world things don't play out the way the odds say they should. If you have pocket aces and someone else has pocket 2s, the 2s can still win if they hit 3 of a kind. What is the driving force that determines whether or not an event will follow the odds?


A single event? Chance.
 
Kroni
 
Reply Thu 10 Dec, 2009 03:20 am
@kennethamy,
In order for probability to be perfectly logical, the results of chance should equal the probability odds when you look at the entire series of events. If the odds of pulling one card from the deck that is a diamond are 25%, then logically when you add up every time anyone has pulled one card from a deck in all of history, exactly 25% of them should wind up being diamonds.
There's no way we can accurately say whether or not this is true, but it seems that many times things do not turn out this way.
 
xris
 
Reply Thu 10 Dec, 2009 06:32 am
@Kroni,
The law of probability relies on the logical law that guides it.

Probably there is no god, probably UFOs are not alien craft,probably the winner will be the favourite. Whose gambling now?

The problem with using it to determine a debate, it can be abused. Science is very good at abusing its laws on probability, if it does not know it will say, in all probability. Science should not, can not be so flippant. If it cant pick a winner, it should not determine scientific facts by these vague assumptions.

Probably someone will disagree with me.
 
odenskrigare
 
Reply Thu 7 Jan, 2010 12:39 pm
@Yogi DMT,
Yogi DMT;101674 wrote:
I understand how simple probability situations function but logically, it doesn't make sense.

Scenario: A coin is tossed and there is a 50% of it landing on heads and a 50% chance that it will land on tails. The probability of getting heads/tails twice in a row is 25% (.5 x .5). This 25% probability refers to the situation as a whole (not to any particular toss in the sequence).

So, a coin is tossed and lands on heads. The next toss is either 50% heads or 50% tails. To overall probability of the situation says that tails is then more likely an outcome, because that would satisfy the higher probability (h+t = 50%, h+h = 25%, t+t = 25%) which would of course be more likely. So after the first toss results in heads, the second tossed is supposedly more likely to be tails when you look at the overall situation regardless of the probability of the 2nd toss alone is half and half... According to probability, the first toss and the probability of the 2 tosses combines determines a different probability for the second toss other than the 1/2 and 1/2 probability of heads and tails.

I know i'm missing something, why is this?


The probability of the compound event of two heads is .25

But for any given trial, what happened to the coin before is entirely irrelevant. It might have landed heads up before, tails up earlier, been in your pocket, stuck to a piece of gum on your boot heel, flattened into a tiny souvenir plate then restored, etc.

and btw there is no cosmic law that makes coins fall heads up if they've fallen tails up for a good long while or vice versa ... it could happen that a coin falls heads up 64 times in a row and though the odds aren't terribly good it could happen

---------- Post added 01-07-2010 at 01:43 PM ----------

xris;109771 wrote:
The problem with using it to determine a debate, it can be abused. Science is very good at abusing its laws on probability, if it does not know it will say, in all probability. Science should not, can not be so flippant. If it cant pick a winner, it should not determine scientific facts by these vague assumptions.


pretty much everything we know is somehow inductive

whether the sun rises tomorrow or whether penicillin and its derivatives kill bacteria ... all the evidence we have for the two is based on some form of inductive reasoning

and btw scientists don't abuse statistics so much as they misuse them (out of ignorance)

and btw statistics when used properly are by no means vague
 
HexHammer
 
Reply Thu 25 Feb, 2010 05:00 pm
@Yogi DMT,
The outcome of tossing a coind should be random.

Random = unpredicable (but still adhereing certain algorithms)
 
Reconstructo
 
Reply Sat 6 Mar, 2010 03:37 pm
@HexHammer,
HexHammer;132531 wrote:
The outcome of tossing a coind should be random.

Random = unpredicable (but still adhereing certain algorithms)


I think you are pointing at an important example. The time factor is key. Ifd we toss an ideal (50/50) coin many times, it's general probability will conform to this 50/50, the moreso the more we toss it?

But I would rather bet on a single coin toss than guess what a single role of a six-sided die would be.
 
HexHammer
 
Reply Sun 7 Mar, 2010 08:03 am
@Reconstructo,
Reconstructo;136953 wrote:
I think you are pointing at an important example. The time factor is key. Ifd we toss an ideal (50/50) coin many times, it's general probability will conform to this 50/50, the moreso the more we toss it?

But I would rather bet on a single coin toss than guess what a single role of a six-sided die would be.
?
Then it wouldn't be random.

:poke-eye:
 
Emil
 
Reply Sun 7 Mar, 2010 08:24 am
@HexHammer,
HexHammer;132531 wrote:
The outcome of tossing a coind should be random.

Random = unpredicable (but still adhereing certain algorithms)


It is only unpredictable to some degree. Some people made a machine, some years back, to determine where a seemingly unpredictable roulette would land and they used that in Vegas for huge profit.
 
HexHammer
 
Reply Sun 7 Mar, 2010 09:56 am
@Emil,
Emil;137174 wrote:
It is only unpredictable to some degree. Some people made a machine, some years back, to determine where a seemingly unpredictable roulette would land and they used that in Vegas for huge profit.
Indeed, that's why we have insurance companies who makes predictions about our seemingly random life, which it really isn't on large scale.
 
Diogenes phil
 
Reply Thu 11 Mar, 2010 09:29 pm
@Yogi DMT,
Probabilty does not stack like dominos. Subsequent changes do not effect current chance, overall probability will still be the same.
 
TranscendHumanit
 
Reply Thu 8 Apr, 2010 09:31 am
@Yogi DMT,
I read Richard von Mises book Probability, Statistics, and Truth. He say there is case probability and class probability, and that only class probability can be logically put into numbers; case probability is subject to judgment. Here is an articleabout Richard von Mises' theory of probability. Also his brother Ludwig von Mises write about it in his book Human Action.
 
sitkaa
 
Reply Mon 10 May, 2010 12:59 pm
@TranscendHumanit,
Whither probability in the moment?

The answer may be found in the storyline, but it occurs in the story.
 
 

 
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