I'm guessing that miners are randomly selected, but I'm curious as to which miner receives the fee for gas paid for each transaction?

In hindsight, the answer to this question is obvious: of course it is the miner that also solves the PoWhash. They get the block reward AND the gas.

The suggested duplicate answer (the questions are also very different actually) does not hone in on the PoW incentive and why a miner is rewarded. The answer for this question targets exactly how the gas is rewarded to the miner.

marked as duplicate by Ismael, Tjaden Hess, Rob Hitchens B9lab, Badr Bellaj, Joël Jun 30 '17 at 3:08

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

[This is possibly a dupe of this question, but I thought it important to address the first part... Feel free to flag it though!]

I'm guessing that miners are randomly selected

Mining is a competition to create a block with a valid proof of work. This proof of doing some work takes the form of solving a mathematical puzzle and broadcasting the answer to the network as proof. The first miner to solve this puzzle wins the competition, and is said to have successfully mined a block.

...which miner receives the fee paid for gas for each transaction?

The miner who successfully mines the block also gets the fee paid for gas from each of the transactions they decide to put into the block.

See:

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