What if you flipped a coin 20 times, and got one of these results? (H stands for heads, and T stands for tails.)

1) HHHHHHHHHHHHHHHHHHHH
2) HTHHTHTHTHTTTHTHTTHH
3) HTHTHTHTHTHTHTHTHTHT

Now, there is only one chance in a million of getting sequence 1. You would look at it and say immediately that something was wrong -- the coin was somehow loaded, or something.

There is, however, only one chance in a million of getting sequence 2, as well. There is only one chance in a million of getting any particular sequence. So there is nothing suspicious about getting a particular sequence unless that sequence is distinctive.

Which leads us to sequence 3. It is distinctive. Is it distinctive enough?

This question has real-world analogues. Probability tells us what the chances are of something happening before it does. We generally, however, want to know after it happened how significant that occurence is.

I choose three volatile stocks. In July, I mail out a prediction that the Smith Company will rise in August to 4,000 potential investors; I mail out a prediction that it will drop in August to 4,000 other potential investors. One of those predictions is correct. To half of those to whom I mailed the correct prediction, I mail the prediction that the Jones Company will rise in September, to the other half that it will fall in September. One of those predictions is correct. To half of those to whom I mailed the correct prediction, I mail the prediction that the Brown Company will rise in October, to the other half that it will fall in October. That gives me 1,000 prospects for my stock-prediction newsletter who know that I've been correct on my last three picks.

If the police get a DNA sample at the scene of the crime, then they can check the DNA of a suspect, or even a dozen suspects. The likelihood of a false positive is less than one chance in a million. There is, however, now a bank of millions of DNA samples on file. The probability of a false positive among them approaches one.

In politics, we have a history of Democratic administrations seeing a higher growth than Republican administrations do. Is that a coincidence, or is that a pattern? This is one of the debates of the current period.

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#### Comment Preferences

• ##### Tip Jar(6+ / 0-)
Recommended by:
CwV, mmcnary, Volt3930, antooo, whaddaya, janmtairy

Democrats are the party of Economic Growth.

• ##### It's a pattern.(3+ / 0-)
Recommended by:

If I ran this circus, things would be DIFFERENT!

• ##### Well, that sure explains(2+ / 0-)
Recommended by:

Those stock tip emails I get.  Only instead of 4000 email, I bet he sends out 4,000,000.

• ##### When I Get One of Those(0+ / 0-)

I watch for the next week. Two weeks ago, the stock I heard about went from \$0.75 to \$2.10 in two days and two days later it was at \$0.42. Jackpot for someone.

Gegen diesen Idioten muss ich verlieren! – Chess Grandmaster Aaron Nimzowitsch (Why must I lose to this idiot!)

• ##### The Key, Of Course(3+ / 0-)
Recommended by:
Ashaman, wilderness voice, Gooserock

is to buy the day before you get the email.

Gegen diesen Idioten muss ich verlieren! – Chess Grandmaster Aaron Nimzowitsch (Why must I lose to this idiot!)

[ Parent ]

• ##### Shroedinger Investment Corp.(4+ / 0-)
Recommended by:
xulon, alypsee1, Frank Palmer, Abelia

You're not broke till you look at your portfolio.

We are called to speak for the weak, for the voiceless, for victims of our nation and for those it calls enemy.... --ML King "Beyond Vietnam"

[ Parent ]

• ##### Fingerprints(1+ / 0-)
Recommended by:
wilderness voice

http://phys.org/...

"In a controlled study, fingerprint examiners who determined that a crime scene-quality print matched a high-quality sample from the same individual were correct 99.8% of the time."

- Wrong two times in a thousand, or two thousand times in a million; so with DNA one time in a million is really good.

- the context also matters, whether with the coin toss, the investor letter, DNA or economic growth.  The mathematical probability by itself doesn't mean much.

• ##### The numerical probability means a hell of a lot.(0+ / 0-)

The problem people have is that they want it to mean something else.

Democrats are the party of Economic Growth.

[ Parent ]

• ##### Bayesian probabilities(0+ / 0-)

Well, what I meant by context is that the value of probability (not its numerical value) depends on how much it helps us separate competing hypothesis.

E.g., given say a dozen people who could possibly be responsible for a crime, say mutually exclusive and equally likely, how much does a finding of a fingerprint that matches one of the persons, a match that is accurate 998 times out of a 1000,  change the probability that that one person is definitely involved in the crime?