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#1
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For the mathematically minded
Hi all, just a quick probability question that I'm not sure about. What are the odds of flipping a coin and having it come up heads every time 21 times in a row?
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#2
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Re: For the mathematically minded
.5^21= ~.00005%
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#3
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Re: For the mathematically minded
[ QUOTE ]
Hi all, just a quick probability question that I'm not sure about. What are the odds of flipping a fair coin and having it come up heads every time 21 times in a row? [/ QUOTE ] FYP |
#4
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Re: For the mathematically minded
[ QUOTE ]
[ QUOTE ] Hi all, just a quick probability question that I'm not sure about. What are the odds of flipping a fair coin and having it come up heads every time 21 times in a row? [/ QUOTE ] FYP [/ QUOTE ] Wow what a wonderful contribution. The probability of any fixed particular sequence of length 21 of heads and tails is (1/2)^21 = 4.76837158 × 10-7. |
#5
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Re: For the mathematically minded
[ QUOTE ]
Wow what a wonderful contribution. The probability of any fixed particular sequence of length 21 of heads and tails is (1/2)^21 = 4.76837158 × 10-7. [/ QUOTE ] Not if you're talking about normal coins. P.S. .5^21 = (1/2)^21 |
#6
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Re: For the mathematically minded
[ QUOTE ]
Wow what a wonderful contribution. [/ QUOTE ] I assume that's sarcastic, although it's hard to tell in message postings. I apologize if I'm wrong. It is an important contribution. Of all the coins in the history of the world that have been flipped 21 times heads in a row, I'll bet none of them were fair. When you see a highly unusual event, it's very likely that the assumptions underlying the computation were wrong. If a coin flips 21 heads in a row, bet on heads next flip. As a theoretical calculation, 0.5^21 is correct. But it's important to state the assumption. |
#7
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Re: For the mathematically minded
[ QUOTE ]
It is an important contribution. Of all the coins in the history of the world that have been flipped 21 times heads in a row, I'll bet none of them were fair. [/ QUOTE ] Assuming "fair" means "between .495 and .505" or some other suitable approximation, I'll take that bet. 5 in 10,000,000 isn't so unlikely that it's never happened in the history of the world. Now, I'll give you a fun example of a claim that hasn't happened in the history of the world. Someone once claimed to me that they were watching for AQ vs AK showdowns on PokerStars all in preflop and made a spreadsheet where they marked the result. They claimed that after 2000 trials, AQ had won 50%. Bill and I estimated the probability of this happening. It was like 1 in all the electrons in the universe. (obviously, either the site is rigged which i doubt or there's a little selection bias problem here) jerrod |
#8
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Re: For the mathematically minded
[ QUOTE ]
Assuming "fair" means "between .495 and .505" or some other suitable approximation, I'll take that bet. 5 in 10,000,000 isn't so unlikely that it's never happened in the history of the world. [/ QUOTE ] I won't give you the 0.495 to 0.505, what I mean is I would bet that the coin has greater than 0.5 chance of coming up heads. It's true the world has been around for a while, but how often does someone flip a coin 21 times in a row? It could well be in the millions, or billions, in which case you're probably right that someone hit 21 heads in a row with a coin that had 0.499999 chance of coming up heads. I got a bit carried away. Let me reduce my bet to, if I saw a coin come up heads 21 times in a row, I would bet that it had greater than 0.5 chance of coming up heads. |
#9
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Re: For the mathematically minded
[ QUOTE ]
[ QUOTE ] Wow what a wonderful contribution. [/ QUOTE ] I assume that's sarcastic, although it's hard to tell in message postings. I apologize if I'm wrong. It is an important contribution. Of all the coins in the history of the world that have been flipped 21 times heads in a row, I'll bet none of them were fair. When you see a highly unusual event, it's very likely that the assumptions underlying the computation were wrong. If a coin flips 21 heads in a row, bet on heads next flip. As a theoretical calculation, 0.5^21 is correct. But it's important to state the assumption. [/ QUOTE ] When people talk about probability problems involving coins they always mean fair coins unless they specify otherwise. It's not close. |
#10
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Re: For the mathematically minded
[ QUOTE ]
When people talk about probability problems involving coins they always mean fair coins unless they specify otherwise. It's not close. [/ QUOTE ] Except when WPT announcers talk about the QQ vs AK "coin flip." Talk about a ridiculously unfair coin. -RMJ |
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