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That is basically the whole question, but to elaborate: I am just getting started to crack into this game and I see a huge difference from planet to planet in what gets "prospected". Sometimes I get lots of fuel and nothing much else. Metals seem to be pretty consistent but sometimes I never get rares and radioactives. I presume rares and radioactives are supposed to be rare, but how rare? Are they more or less common depending on the planet, not just how much you prospect or how good your leaders are.

From the manual, section 5.5.4.1:

"Fuel/Oil resource Hexes can be found and mined if Planet has had a
history of organic life. Otherwise it will need to be synthetically produced."

"Metal resource Hexes can be found and be mined. They are
more abundant on Planets with more heavy cores."

"Rare Metal resource Hexes can be found and be mined. They
are more abundant on Planets with more heavy cores."

In the Reports tab, under the Help tab, you can go to the Planet Statistics Overview and there is a stat called "Heavy elements". To my understanding this is effectively a measure of the "Planets with more heavy cores" metric mentioned in the manual.

There is one more aspect to consider. During the colonization history of the planet, there may have been significant mining activity. To my understanding, the more mining activity during colonization, the less untapped metal deposits will be available.

In terms of just how much more 'rare' are rare metals and radioactives compared to metal deposits --- I don't have any solid info. Anecdotally, I would say my average has been 1 rare metal deposit for maybe every 2 metal deposits found. Maybe about the same ratio or less for radioactives. My impression is that if you find metal, you will eventually find rare and radioactive, given a large enough territory. Also keep in mind that depending on starting settings (difficulty, tech, zones) you (and major AIs) get water and metal deposits placed nearby your starting city.

Hope that helps a bit. Maybe someone will have a more complete answer.

Thank you, exactly what I was looking for. Did not see that in the manual.