Polling

kuwisdelu

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Incidentally, all of the odds C-3PO tells Han are backwards.

Presumably, no one ever pointed out this flaw in his programming to Anakin.

The odds of successfully navigating an asteroid field are actually 1 to 3,720.
 

Wye Pen

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Kuwisdelu, according to the law of big numbers:

if you toss an unbiased coin,

the probability that the number of heads is approximately equal to the number of tails is 1 (as the number of tosses increases).

What is the probability that the number of heads is exactly equal to the number of tails ?
 

RichardGarfinkle

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Kuwisdelu, according to the law of big numbers:

if you toss an unbiased coin,

the probability that the number of heads is approximately equal to the number of tails is 1 (as the number of tosses increases).

What is the probability that the number of heads is exactly equal to the number of tails ?

Okay. Here goes the math.

If you flip n coins, there are 2^n possible sequences. For a sequence to have exactly k heads is the equivalent of choosing which k out of the n slots are filled with heads. The number of such sequences is n!/(n-k)!k!. So the probability is (n!/(n-k)!k!)/2^n

Regardless of which choice of k you make 2^n gets large much faster than n!/(n-k)!k! so unless I'm messing up somewhere, the limit as n goes to infinity of (n!/(n-k)!k!)/2^n = 0. So in the long run, the answer is 0.
 

Wye Pen

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These two probabilities should be either very close to each other or the same. Surely something is making the discrepancy between the two unacceptable.
 

RichardGarfinkle

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These two probabilities should be either very close to each other or the same. Surely something is making the discrepancy between the two unacceptable.

No they aren't close at all. You need to look at the distribution of probabilities. As n increases the number of possible configurations increases as well. As a result the normal curve expands horizontally as well as vertically. Here are the first few values.

n coins number of configurations number of configurations that are exactly half heads probability
2 4 2 0.5
4 16 6 0.375
6 64 20 0.3125
8 256 70 0.2734
 

raburrell

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n! is n factorial - it's n*(n-1)*(n-2)*...(1) eg: 4! would be 4*3*2*1 = 24.
 

StuToYou

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Getting flashbacks to sexy sigma signs and bulbous bell curves - ugh.

A recent splendorous example of getting it wrong was the DEM predictions in Michigan.

Great work RG and Kusw etc
 
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Brad S

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It seems that more often than not, polls can be used to shape, as much as report, public opinion. And since the general public will rarely (if ever) take the time to look into the methodology of polling, it's sad that it has become such a staple of modern journalism.