I would do additional conditioning. So P(opera | farmer), P(museum | opera, farmer), P(chess | museum, opera, farmer), etc.My guess would it would look something like:P(opera | farmer) = 5% (does anyone actually like opera?)P(museums | opera, farmer) = 95%P(chess | m, o, f) = 40%So 5% * 95% * 40% = 1.9% of farmers...P(o | t) = 80%P(m | o, t) = 50%P(c | m, o, t) = 20%So 80% * 50% * 20% = 8% of trumpet players...Which is a likelihood ratio ~.25 so I end up with something like 125 to 1 that we’re talking to a farmer.
I would do additional conditioning. So P(opera | farmer), P(museum | opera, farmer), P(chess | museum, opera, farmer), etc.
My guess would it would look something like:
P(opera | farmer) = 5% (does anyone actually like opera?)
P(museums | opera, farmer) = 95%
P(chess | m, o, f) = 40%
So 5% * 95% * 40% = 1.9% of farmers...
P(o | t) = 80%
P(m | o, t) = 50%
P(c | m, o, t) = 20%
So 80% * 50% * 20% = 8% of trumpet players...
Which is a likelihood ratio ~.25 so I end up with something like 125 to 1 that we’re talking to a farmer.