Suppose there is mining pool XYZ. 10 miners, 1 through 10, are subscribed to it and miners have varying hash power. Some have 10 GPU mining rigs, while others have just a single CPU running 24 hours a day seven days a week. Suppose 12.5 BTC are won by XYZ each week.
Does it mean that each week one of those 10 miners win 12.5 BTC and XYZ then distributes BTC to each of the 10 miners in accordance with their contribution of hashing power?
Or does XYZ gather together hashing power of miners 1 to 10 to try to be the first to solve the puzzle to win 12.5 BTC ?
Is it possible for a solo miner with 10+ GPU rig to win 12.5 BTC block reward even though mining pool XYZ has a much greater combined hashing power? I mean is there randomness also involved in winning the block reward in addition to hashing power?