Coin flips.
September 3rd, 2011 at 8:34:53 PM
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I flip a coin 10 times and get heads 10 times.
I say the possibility of getting heads 10 times in a row is very small and therefore their is a chance of bias in the coin. Is their a way of working out the bias?
I say the possibility of getting heads 10 times in a row is very small and therefore their is a chance of bias in the coin. Is their a way of working out the bias?
September 3rd, 2011 at 8:54:45 PM
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Assuming a fair coin, the bias is 0.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 3rd, 2011 at 8:56:20 PM
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but you do not know if it is a fair coin or if it is a biased coin.
September 3rd, 2011 at 9:27:42 PM
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Quote: Catprogbut you do not know if it is a fair coin or if it is a biased coin.
May I rephrase the question this way: One coin in a 1,000 has a heads on both sides. You toss a random coin 10 times and it is heads every time. What is the probability you were flipping a two-headed coin?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 3rd, 2011 at 9:30:56 PM
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1 in 1000.
"It's not called gambling if the math is on your side."
September 3rd, 2011 at 9:46:32 PM
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Quote: EvenBob1 in 1000.
Nope.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 3rd, 2011 at 10:57:40 PM
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No fair asking more questions! We have a cat stuck in a safe that we still don't know the fate of!
Edit: about 1 in 4?
Edit: about 1 in 4?
The opinions of this moderator are for entertainment purposes only.
September 3rd, 2011 at 11:13:36 PM
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Quote: WizardMay I rephrase the question this way: One coin in a 1,000 has a heads on both sides. You toss a random coin 10 times and it is heads every time. What is the probability you were flipping a two-headed coin?
About 50%.
Old enough to repaint. Young enough to sell.
September 3rd, 2011 at 11:33:04 PM
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Quote: CatprogI flip a coin 10 times and get heads 10 times.
I say the possibility of getting heads 10 times in a row is very small and therefore their is a chance of bias in the coin. Is their a way of working out the bias?
There is no bias and 10 in a row is not a rare thing ...
You can find 3 std being very common running simulation and explore the law of series - nothing is due to happen - still there is no bias.
Just common natural fluctation.
Off-Topic >>>
If you find 10 in a row intressting you can read about "the law of series" but note its not a law - it is only observations.
If you like even money i would just say there exist no math way to explore does with any kind of andvantage.
And random against random does not work - just lame.
But if you want to know how to get imbalance and balance measuring the distribution of coin flips - then you should read Marigny - there is no other deeper and better work that has been made in world history about the subject.
But then again you will probably only find my writings with simulations softwares using googel :-)
How do they say it - been there - done that - ain't working LOL
And if you see 10 in a row and you life depends on it - i would follow the 10 in a row and not play against them - even if there still is 50/50.
AP - It's not that it can't be done, but rather people don't really have a clue as to the level of fanaticism and outright obsession that it takes to be successful, let alone get to the level where you can take money out of the casinos on a regular basis. Out of 1,000 people that earnestly try, maybe only one will make it.
September 4th, 2011 at 4:01:46 AM
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Catprog, I think you are 'getting the treatment' here because your question reveals a little naivety. Chances a fair coin would repeat the same result 10 times in a row is one in 1024. That is somewhat unusual but if you call your local TV station they arent going to send over a reporter and cameras and everything to interview you. Here is a Wizard recommended site to help you do simple calculations like this yourself.
Revealing my own ineptitude, I can see the probability of it happening with a fair coin being one in 1024, and 100% with a two headed coin, but I can't take that information and answer your more interesting question. Perhaps I should take my own advice and go to the math goodies link, but as Catprog can no doubt tell you, that's probably not going to happen [g]
Quote: WizardMay I rephrase the question this way: One coin in a 1,000 has a heads on both sides. You toss a random coin 10 times and it is heads every time. What is the probability you were flipping a two-headed coin?
Revealing my own ineptitude, I can see the probability of it happening with a fair coin being one in 1024, and 100% with a two headed coin, but I can't take that information and answer your more interesting question. Perhaps I should take my own advice and go to the math goodies link, but as Catprog can no doubt tell you, that's probably not going to happen [g]
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell! She is, after all, stone deaf. ... Arnold Snyder
September 4th, 2011 at 5:42:14 AM
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Well if odiousgambit won't turn to Excel, or even a calculator, I will.
In the Wizard's example, 1/1000 times you'll pick up that dang double header. The other 999 times, you've got a 1/1024 chance of 10 heads in a row.
Therefore, the chance that, in 1000 trails of picking a random coin and flipping 10 times, of seeing 10 heads would be: .001000 + .975585 = .976585
Therefore, the chance of it happening once is .000976 or 1 in 1023.975
In reality, since there are far fewer than 1 in 1000 double headed coins in circulation, the chance of picking a coin and getting 10 heads in row is damn near 1 in 1024. So I kinda think my result is correct.
In the Wizard's example, 1/1000 times you'll pick up that dang double header. The other 999 times, you've got a 1/1024 chance of 10 heads in a row.
Therefore, the chance that, in 1000 trails of picking a random coin and flipping 10 times, of seeing 10 heads would be: .001000 + .975585 = .976585
Therefore, the chance of it happening once is .000976 or 1 in 1023.975
In reality, since there are far fewer than 1 in 1000 double headed coins in circulation, the chance of picking a coin and getting 10 heads in row is damn near 1 in 1024. So I kinda think my result is correct.
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
September 4th, 2011 at 5:47:08 AM
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I can't see how the chance can be greater than one in a thousand. If there's a thousand coins, and one is double sided, there has to be at least a one in thousand chance of selecting a coin at random and getting ten heads in a row.
I make in about in 1 in 506.
1/1000 x1.... Picking the biased coin.
999/1000 x 1/1024.... Picking a fair coin.
Sum : 0.0019755 = 1 in 506
Dj, I think in your sums you set the average number of occurrences to get the biased coin in 1000 trials to 0.001, not 1.
I make in about in 1 in 506.
1/1000 x1.... Picking the biased coin.
999/1000 x 1/1024.... Picking a fair coin.
Sum : 0.0019755 = 1 in 506
Dj, I think in your sums you set the average number of occurrences to get the biased coin in 1000 trials to 0.001, not 1.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
September 4th, 2011 at 7:24:08 AM
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Quote: thecesspit...I make in about in 1 in 506....
What a coincidence! I get 0.506, which is close to waltomeal's answer.
September 4th, 2011 at 7:44:00 AM
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Quote: ChesterDogWhat a coincidence! I get 0.506, which is close to waltomeal's answer.
That is correct. Here is the pertinent formula:
Pr(two headed coin given 10 heads observed) = prob(two headed coin and 10 heads observed)/pr(10 heads observed) =
(0.001*1)/(0.001*1 + .999*(1/2)^10) = 0.506178942.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 4th, 2011 at 7:45:35 AM
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Quote: ChesterDogWhat a coincidence! I get 0.506, which is close to waltomeal's answer.
Ditto: 0.506178942
Edit: :) I type really slow.
Man Babes #AxelFabulous
September 4th, 2011 at 7:54:51 AM
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Quote: WizardMay I rephrase the question this way: One coin in a 1,000 has a heads on both sides. You toss a random coin 10 times and it is heads every time. What is the probability you were flipping a two-headed coin?
.001(1) / [.001(1) + .999(.5^10)] = .5062
edit: you guys beat me.
September 4th, 2011 at 9:58:12 AM
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Quote: ChesterDogWhat a coincidence! I get 0.506, which is close to waltomeal's answer.
I answered the wrong question, I think. What's the probability of selecting a coin and flipping ten heads, given 1000 coins, one of which is double headed... Eg what's the probability of the event occurring, not what was the cause of the event.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
September 4th, 2011 at 11:24:16 AM
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Quote: thecesspitI answered the wrong question, I think. What's the probability of selecting a coin and flipping ten heads, given 1000 coins, one of which is double headed... Eg what's the probability of the event occurring, not what was the cause of the event.
0.001*1 + 0.999*(1/2)^10 = 0.0019756.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 4th, 2011 at 10:45:03 PM
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Quote: odiousgambitCatprog, I think you are 'getting the treatment' here because your question reveals a little naivety.
Ok then. new question.
I have x fair coins and y coins which are doubled headed.
I pick a coin and flip it 30 times and get heads all the time.
Given that 30 heads in a row is 1 in 1,073,741,824 on a fair coin what are the chances that I picked a doubled headed coin.
September 4th, 2011 at 10:52:21 PM
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Quote: CatprogOk then. new question.
I have x fair coins and y coins which are doubled headed.
I pick a coin and flip it 30 times and get heads all the time.
Given that 30 heads in a row is 1 in 1,073,741,824 on a fair coin what are the chances that I picked a doubled headed coin.
Pr(two headed coin given 30 heads observed) = prob(two headed coin and 30 heads observed)/pr(30 heads observed) =
((y/(x+y)*1)/((y/(x+y)*1)*1 + (x/(x+y)*1)*(1/2)^30)
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 4th, 2011 at 11:01:42 PM
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Quote: Wizard0.001*1 + 0.999*(1/2)^10 = 0.0019756.
Which is the 1 in 506 answer I gave :)
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
September 5th, 2011 at 4:09:14 AM
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Quote: thecesspitWhich is the 1 in 506 answer I gave :)
Yes but it wasn't asked.
September 5th, 2011 at 7:23:46 AM
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Quote: Jufo81Yes but it wasn't asked.
Yes, I acknowledged that..... And the wizard then calculated the same answer to the question -I- thought had been asked...
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
