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?

Re: For the mathematically minded
 

.5^21= ~.00005%

Re: For the mathematically minded
 

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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?


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FYP

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?


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FYP

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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.

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.

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Not if you're talking about normal coins.

P.S. .5^21 = (1/2)^21

Re: For the mathematically minded
 

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Wow what a wonderful contribution.

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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.

Re: For the mathematically minded
 

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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.

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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

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.

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Jason_T

You surprise me. Usually you surprise me because I'm wrong. I have great respect for both your talents and insight -- but do you really see this correction of an assumption as trivial?

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?


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FYP

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it is very obvious he is talking about a fair coin.

sorry you wasted your FYP

Re: For the mathematically minded
 

So, now that this question has come up...

How many fans of Tom Stoppard's Rosencrantz and Guildenstern are Dead do we have in the house?