RAIMIUS wrote:
FEOS wrote:
If there are ten die and you roll all ten at once, you've got a 1/6 chance every time you roll the set.
I haven't taken stats in a while, but I'm sure that is incorrect. Think about it. You would have a 1/6 chance that any, single die would be a 6 (and a 1/6 x 10 chance that some one of them would be a 6) but the chances of them ALL being 6 on one roll is still (1/6)^10...there is only one set in 6^10 possiblilities that is ALL sixes.
I'm sure it's not incorrect--I just clearly did a poor job of explaining, as evidenced by Fodder's comment:
PureFodder wrote:
Again the chances of rolling ten consecutive 6s is (1/6)^10. the chances of rolling 10 dice and getting all sixes is (1/6)^10.
The way you roll the dice makes no difference whatsoever.
If you roll all the dice at once, the odds of any single die coming up a six (failure of the system) is the same as if you rolled a single die (1/6), because each roll is independent of the others. In PureFodder's scenario, any single failure of a step along the way will result in an overall system failure (sort of like an <AND> function). So the odds of an overall system failure are 1/6.
In a serial situation (you can't roll the following die unless the previous die comes up six), it is cumulative up through the last die rolled. The odds for the first die are 1/6. The odds for the second die are 1/6, but you can only attempt the try if the first one comes up six. So there's only a 1/6 chance you will even get to the next 1/6 chance. And so on. Therefore, with ten dice, there is only a (1/6)^10 chance of rolling through the entire set of dice with a six on the first attempt for each. Chance of overall system failure is (1/6)^10.
Regardless, PureFodder's assumption of how the process works (parallel) induces more risk of compromise of the process. The reality of the process (serial) ensures a better chance of catching a failure at any point along the way.
PureFodder wrote:
My point is that the US system has a potential for disaster. The Russian one is presumed to be even worse. They are both an issue.
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You seem to be under the assumption that a mistake could only result in a single US missile being launched, but a series of unlikely errors in the intel could result in a full lauch being intentionally carried out as the right response to the intel which is unfortunately filled with errors.
Then you are crediting the nuclear C2 system for errors in the intel system. They are separate and distinct. I was talking specifically about the nuke C2 system. In the situation you describe (intel errors), the failure is not in the nuke C2 system...it would work as specified.