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Cyan comments on Open Thread: February 2010 - Less Wrong
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Anyone willing to give some uneducated fool a little math coaching? I'm really just starting with math and I probably shouldn't already get into this stuff before reading up more, but it's really bothering me. I came across this page today: http://wiki.lesswrong.com/wiki/Prior_odds
My question, how do you get a likelihood ratio of 11:1 in favor of a diamond? I'm getting this: .88/(.88+7.92)=.1 thus 10% probability for a beep to be a box containing a diamond? Since the diamond-detector is 88% likely to beep on that 1 box and 8% likely to beep on the 99 boxes containing no diamonds. So you have 7.92 false beeps and .88 positive ones which add up to 8.8 beeps of which only .88 are actually boxes containing a diamond?
As of today I'm still struggling with basic algebra. So that might explain my confusion. Though at some point I'll arrive at probability. But I'd be really grateful if somebody could enlighten me now.
Thanks!
The likelihood ratio is Pr(beep | diamond) / Pr(beep | empty) = 0.88/0.08 = 11. I was going to say you ought to read the link for "likelihood ratio", but there's nothing there, so you should try the other wiki.
Also, don't think of running the detector over every box; think of testing one box at random.