I’m using the data from the CIA’s example (see link at the end). I’m sure that in a real-life situation things would be more complex. Also, I think that what they imply is that both the Vietnamese and Cambodian use the same planes (Soviet-made), so the witness is tested on how well he recognizes the markings on the planes and not plane types.

I put a picture of a MiG 19 on top because it is one of the planes used in the war, but I didn’t do the research to see if both Cambodia and Vietnam used those. I know MiG 17 and 21 were more frequent, though.

Very good observation about the second example. Scary stuff, really.

I have two observations. In the first example, you don’t actually give the Bayesian probabilities for false alarms from the actual data, and assume that in each case it is 0.8. More likely, they will have differnent false alarm rates. Imagine for instance that all of the Migs were correctly identified and that 30% of the Cambodian a/c. This would bring your probability of a correct Cambodian sighting down to about 10%.

In the second example, the statistic that scares me is that of those who get a second mamogram (standard procedure when you have an initial positive as you show) about 90 women out of 10,000 will have TWO false positives, and then be put on the track for having to treat breast cancer until found otherwise. Furthermore, 7 of those with breast cancer will have a second false negative. You are thus left with a conundrum in either case after the first positive.