Question regarding probability

[Vault101]

I don't know much about probability and the maths surrounding it...

for no real reason just now I've been thinking about something and I'm a bit confused mabye any maths nerds can help me out

1. ok first "thing" (theory, rule I don't know) is that I think I once heard the more time that passes, the higher the probability of something happening gets. This is kind of part of how life came about....it just took a really really long time for the unlikely "thing" to happen (not sure that was) or to put it another way I think I once saw on a documetry that its not impossible for sand blown by the wing on a beach to arrange itself into a sandcastle by pure chance....its just incredibly unlikely and the time required for that probability to come about is alot (maybe more time than the universe has)

2. this second thing Ive heard I think someone here referred to it as "gamblers fallacy" as in if a gambler is betting on "heads or tales" and it keeps getting heads over and over and over the gamblers Idea is that "its gonna get tails the NEXT one" <-repeat untill they end up boke, I think the fallacy is that the probability of heads or tales is independent

these two Ideas seem to contractict each other

so If I'm still making sense would anyone care to explain/tell me where I got it wrong? ;p

 

[Keoul]

The probability of heads or tails is not independent.
The rule/theory/whatever with your second statement is that the probability of continuously getting heads in a row decreases with each successful heads, so the chances of getting tails increases, which follows your first theory
I could go find a fancy diagram if you still don't get it.

 

[Thaluikhain]

They don't, not really.

Taking each toss of the coins individually, it's only ever going to be 50%. If you've gotten 10 heads in a row, you've got a 50% chance of getting tails. It's getting to that point which is hard.

Or, to look at it another way, you don't know when the gambler will get tails, but if they keep trying, sooner or later they'll get it.

EDIT: Oh, the probability of anything happening that actually has is 100%. So, toss a coin, and you have a 50% chance of getting tails. If you do get tails, then the chances of you getting tails for that toss is 100%, because it's happened.

 

[BringBackBuck]

I think you are confusing chance and probability.

Probability measures the likely outcome over x number of attempts (as in your first example), so the probability of something happening will increase as the number of attempts increases.

Chance is the odds that a specific thing will happen on any given attempt, eg: 1/6 chance of hitting a 6 when you roll a die.

So whilst it is likely (probability) that given six attempts at rolling a die you will get a 6, if the first 5 numbers are not sixes, there is no certainty that the sixth throw will yield the result you are after, in fact it is no more likely than any other number (chance). Betting because a 6 "is due" is the gambler's fallacy.

 

[Hagi]

Gambler's fallacy is pretty much people misinterpreting the first rule.

If we throw a coin ten times then the chance of getting tails at least once is 99,9%. Some people take this to mean that if you've thrown heads 9 times then somehow your next throw will magically have a 99,9% chance of turning up tails.

You can't include past outcomes in your calculations because they, obviously, don't influence future outcomes.

If you throw your first coin and it turns up heads then your chance to throw tails at least once in your remaining nine throws doesn't stay at 99,9%, it decreases because some of the possible outcomes (the ones that have you throwing tails on your first throw) become impossible. Just like if you throw tails on your first throw then the chance becomes 100% because you've already thrown that one tails.