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Lumifer comments on Open thread, Feb. 01 - Feb. 07, 2016 - Less Wrong Discussion
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Let's say I make six predictions or statements that I believe to be true about someone I've never met and I say the statements taken as a whole are true with P = 0.7. Note that I do not claim to be psychic.
The P of each statement must then lie between 0.7 and 1.0, and if they are equal then the P of each statement is 0.7 ^ (1/6) = 0.94. Let's say 0.9 because I doubt any statement about this type of probability should be reported with two significant figures, and perhaps even one significant figure without an attached tolerance band is a bit of a stretch.
I'd say that a P this high for each statement, given this example, is well nigh impossible.
Agreed?
Maybe I'm not so underqualified as to be unable to enjoy this forum.
You mean that all the statements are true -- right? You're evaluating "a AND b AND c AND d AND e AND f"?
Correct.
You are assuming the statements are independent of each other. That's not necessarily so.
To take an extreme example, all six statements could be a function of the same single property/event. In such a case the P of each is 0.7 and the P of all of them is still 0.7.