Percentage of high school seniors who participated in various school-related extracurricular activities, by sex: 1990 and 2001 - https://nces.ed.gov/programs/youthindicators/Indicators.asp?...

If artistic ability has a strong influence on intelligence compared to athleticism, then P(intelligent | artistic) >= P(intelligent | athletic). We know that P(athletic) > P(artistic) from the data.

By Bayes' theorem:

P(intelligent | artistic) = P(artistic | intelligent) * P(intelligent) / P(artistic).

P(intelligent | athletic) = P(athletic | intelligent) * P(intelligent) / P(athletic).

Ignoring P(intelligent) for a sec, we find

P(intelligent | artistic) ~ P(artistic | intelligent) / P(artistic)

P(intelligent | athletic) ~ P(athletic | intelligent) / P(athletic)

If we accept the assumption that artistic ability is a bigger influence, then

P(artistic | intelligent) / P(artistic) > P(athletic | intelligent) / P(athletic)

Because P(athletic) > P(artistic),

P(artistic | intelligent) > P(artistic) * P(athletic | intelligent) / P(athletic)

P(artistic)/P(athletic) must be less than 1, so we get

P(artistic | intelligent) > P(athletic | intelligent)

I'm not really sure where I was headed with this, but it was neat to think about. If anyone spots an error please just correct me.