# "I would expect this sentence only after another..."

https://arbital.com/p/56n

by Eric Rogstad Jul 7 2016

All three observations are independent as far as you know $$that is, you don't think Betty's any more or less likely to be late if she's driving the blue car, and so on$$\. Each observation — red car, honking, punctuality — carries a $2 : 1$ likelihood in favor of the driver being Betty\. If the red car is punctual and honks at you, but you can't yet see the driver, then your odds that the driver is Betty should be about $8 : 1,$ because, by Bayes' rule you should multiply three $2 : 1$ likelihood ratios together\. But let's say you only get to make two of the observations — your plane lands late, so you don't get to see whether the car was punctual\. Given only two pieces of evidence, your odds that the driver is Betty should be about $4 : 1.$

I would expect this sentence only after another telling me that the observations were red car, honking, and punctuality. I think the next sentence should be broken apart and this should be inserted inside.