a problem about probability

[AAAintheBeltway]

Quote from hardrock375:



The probability of the coin landing on heads ten times in a row is relatively small. The probability of this happening is made up of a series of events occurring. That is, the probability of the coin landing on heads, once, twice, thrice, four times, and so on. The key is, you have to bring all these events together and look at them as a series, rather than each being a separate throw. So, that is why the probability of flipping heads ten times in a row is so low.

The other question is what is the probability of flipping heads on the tenth try, after all the previous ones have been heads? The answer is 1/2, or 50%. Assuming the coin is fair, there are only two outcomes, heads being one, tails, the other. No matter what has happened during the series, the chance of the tenth flip being a head is 50%. Here we are not looking at the flip in a series, but as an independent event. The key phrase in this instance is "tenth try". We are looking at one event, not a series.

Ok, this is what I meant by knowing it is correct and actually understanding it. Ten in a row and the actual tenth coin toss are separate events but what determines which one should control our bet? Intellectually I understand that the tenth toss is 50/50, but there is also a very low probability that the tenth toss will be heads. So which is the better bet?

Isn't fading the tenth throw basically what selling options premium is all about? We can't know the outcome of any particular day ahead of time but we know the results over time form a distribution curve and we are prepared to take on the risk that price stays within that curve.

 

[tomf]

Quote from aphexcoil:



Actually, if the first 10 were heads, then the probability of getting 11 in a row is now 50/50.

hehe, actually yes... but getting the chance for a SERIES of 11 consecutive heads is 0,048%

 

[tomf]

Quote from AAAintheBeltway:



Ok, this is what I meant by knowing it is correct and actually understanding it. Ten in a row and the actual tenth coin toss are separate events but what determines which one should control our bet? Intellectually I understand that the tenth toss is 50/50, but there is also a very low probability that the tenth toss will be heads. So which is the better bet?

You shouldn't bet on the following .. let's say you have 10 consecutive losses with your trades..... because the probability of 11 consecutive losses is so small you load up all your money and go long.

But now you missed the probability for the trade to be a winner is still only 50% .. and not something like 100% - 0,048% = 99,952% --- whow if that was the case i'd only wait for 10 consecutive losses =))

 

[0008]

Quote from tomf:



You shouldn't bet on the following .. let's say you have 10 consecutive losses with your trades..... because the probability of 11 consecutive losses is so small you load up all your money and go long.

But now you missed the probability for the trade to be a winner is still only 50% .. and not something like 100% - 0,048% = 99,952% --- whow if that was the case i'd only wait for 10 consecutive losses =))

If it was the case, we should try to make 9 very small losses, then bet the 10th with all our money and made a fortune!

It simply won't work!

 

[AAAintheBeltway]

tomf,

I have read systems developers advocating something like that. Either wait for a drawdown to start trading the system or only take trades after ,eg, three losing trades or whatever. I tried backtesting that approach but could never make it work. Perhaps it is not statistically sound at all.

 

[OPTIONAL777]

Quote from 0008:

If I toss a coin. What it the chance that I get 10 consecutive heads (or tail)? Is it (1/2)^10=0.00097?

Many people think, if you see 9 consecutive heads, than the chance seeing next one is head is extremely small. And you should bet tail. But some people said, the chance is still 1/2 because they are independent.

I am getting confused. Some math wiz bother to explain?

In Vegas, if you get 10 consecutive heads, you get a comp head job.

 

[tomf]

Quote from AAAintheBeltway:

tomf,

I have read systems developers advocating something like that. Either wait for a drawdown to start trading the system or only take trades after ,eg, three losing trades or whatever. I tried backtesting that approach but could never make it work. Perhaps it is not statistically sound at all.

well, interesting approach ... but they miss the actual probabilities.. so I think this hardly will work out.. because the 10th trade can as well be a loser REMARK: afterall it has a chance of 50% to be a winner .. nothing more nothing less.

 

[axeman]

I saw a Dilbert once where ratbert called "Edge" on
Dilberts next coin toss to prove he was psychic
and it DID land on its edge... hilarious.

peace

axeman

Quote from marketsurfer:




don't forget the possibility of the coin landing on its edge.

have a great new year !

surf

 

[Corallus]

Quote from aphexcoil:

Which do you feel is more likely to happen over 10 tosses?

a: TTTTTTTTTT
b: THTTHTHHTT

They are equally likely since each is a unique probability series both consisting of 10 independent throws (where the probability of either heads or tails on any one throw was 50/50). The mind wants to believe that "b" is more likely, but it isn't.

Here's another thought:

If a friend and I each play one California super lotto ticket and we choose the numbers as follows:

Friend: 23 12 7 19 29 39, Mega # 18

Me: 1 2 3 4 5 6, Mega # 7

Who is more likely to win?

 

[profitseer]

Quote from Corallus:



They are equally likely since each is a unique probability series both consisting of 10 independent throws (where the probability of either heads or tails on any one throw was 50/50). The mind wants to believe that "b" is more likely, but it isn't.

Here's another thought:

If a friend and I each play one California super lotto ticket and we choose the numbers as follows:

Friend: 23 12 7 19 29 39, Mega # 18

Me: 1 2 3 4 5 6, Mega # 7

Who is more likely to win?

one time I pick 1,2,3,4,5 at Keno. The waitress shakes her head and says, "I've been working here three years and I've never seen that come up."

I say, "Then please tell me which 5 numbers come up often."

(don't forget when you're working probabilities to consider the large number factor. I forget what mathematicians call it. It means what works for large numbers won't necessarily work for a series of 10 bets.)