Testwiki:Reference desk/Archives/Mathematics/2012 January 23

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January 23

Related probabilities

If 15% of drivers involved in automobile accidents are not wearing a seat belt at the time of their crash, yet they account for 27% of accident fatalities amongst all drivers, then we can compute that an unrestrained driver is ( 0.27 / 0.73 ) / ( 0.15 / 0.85 ) = 2.1 times more likely to die if they have an accident, right? What is this sort of calculation called, and do we have an article on it? -- ToE 00:27, 23 January 2012 (UTC)

conditional probability. Bo Jacoby (talk) 08:03, 23 January 2012 (UTC).

Thanks; that's exactly what I was looking for. Does this particular manipulation

$\frac{P(A|\mathrm{\neg }B)}{P(A|B)}=\frac{P(\mathrm{\neg }B|A)/P(\mathrm{\neg }B)}{P(B|A)/P(B)}$

(easily derived from Bayes' theorem) get used enough in some circles to be given its own name. -- ToE 01:03, 24 January 2012 (UTC)

With some rearrangement of the terms this becomes Bayes' rule. (The roles of A and B are interchanged in that page). -- Meni Rosenfeld (talk) 16:21, 24 January 2012 (UTC)

Not in my circles. Bo Jacoby (talk) 12:28, 24 January 2012 (UTC).