Chance of 3 people developing Cancer

[DougShrapnel]

Basic question for you guys. In the paper today, a cancer cluster was said to be found. They stated that the chance of someone developing this type of brain cancer was 7 in 200,000. 3 people developed that type of cancer in a small population. What are the chances that 3 people in a population I over-estimate at 1,000? The population is more likey to be in the low hundred but I'm just interested in getting the idea of how to do the problem.

Becuase I'm an idiot I did this
((1 / 28 571) * (1 / 28 571) * (1 / 28 571)) * (1 000 choose 3) = 7.12473073 × 10-6

Am I anywhere close?

[FlFishOn]

This is the 'Big statistical past-posting fraud'. The probability that this occured is 1, certainty, it occured*. That is wholely unrelated to the chance that it occurs next week in another town of 1000 (or again in the same town).

* Upon reflection, I realized we're talking about the news media here. I'm revising the odds, using the Jason Blair adjustment, to three quarters. Upon further reflection, I'm sure if there were 2 identical cancer cases and one that was similar or close, the news media would prevaricate. Probability now at 1/2. Is Dan Rather involved? If so, divide by 5.

P.S. If you really want to learn how to do the probability question you outline then there is a time issue left unaddressed. There is some cancer occurance / unit time factor that would be needed. Then you need to rephrase the question "what are the odds this occurs within a year/month/etc?"

[DougShrapnel]

I searched "'Big statistical past-posting fraud'" on google and only got horse racing related gambling stuff.

[ QUOTE ]
If you really want to learn how to do the probability question you outline then there is a time issue left unaddressed. There is some cancer occurance / unit time factor that would be needed. Then you need to rephrase the question "what are the odds this occurs within a year/month/etc?"

[/ QUOTE ] News bias aside, I'am more interested in understanding how to approach the problem. The 7 in 200,000 number is in a lifetime, I would imagine. Lets use that time frame. If the first number is "correct" with regards to an isolated 1,000 population, I am guessing that I would need to include the number of "populations" within the US in order to get some sort of statistical anylasis for how likely we are to notice an aberation of this magnitude.

[FlFishOn]

"I searched "'Big statistical past-posting fraud'" on google and only got horse racing related gambling stuff."

Past posting is betting, using, researching an event that's already occured. You know the outcome and then you pretend you do not.

Regarding the rest of your question, you're chasing rainbows. There's a deal called the law of large numbers. If you have a really large number of observing opportunities, eventually you'll observe anything. Things that look like 100,000,000 to 1 shots come in all the time if you have 100,000,000,000 chances to observe them.

[DougShrapnel]

[ QUOTE ]
There's a deal call the law of large numbers. If you have a really large number of observing opportunities, eventually you'll observe anything. Things that look like 100,000,000 to 1 shots come in all the time if you have 100,000,000,000 chances to observe them.

[/ QUOTE ] Ok granted, I'm an idiot, but I think I understand this. Perhaps you are trying to be nitty on purpose, which always gives me a good laugh. But I don't see any reason why we can't determine how long of a shot it is, because it happened should be no barrier to getting that probablity. If the flop comes all red, I'm still able to figure out the prob of that happening regardless of the fact that it allready happened, or that I've seen 9 flops.

[FlFishOn]

" Perhaps you are trying to be nitty on purpose, which always gives me a good laugh. "

Yup. I do that.

Ask yourself what it is you wish to know. If you calculate that the odds of this event OCCURING AGAIN IN THE FUTURE SOMEWHERE ELSE are 10^8 - 1 per year against then what have you learned? Almost nothing regarding the actual event.

If you are interested in statistical methodology, start smaller and build up.

[DougShrapnel]

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