Hello,
I am new in coinbase, just now I made a transfer from coinbase address to my personal wallet address. All I have in coinbase is 0.03908 BTC, and I found that I can send this full amount out of coinbase, and I got full amount of 0.03908 BTC to my personal wallet address. But I checked the transaction on blockchain and found the fee is 0.0009 BTC(Fee: 0.0009 BTC - Size: 1837 bytes). I am confused, did coinbase pay this fee for my transfer?
Yes that is true. Coinbase pays the transfer fee and I prefer to use coinbase for this reason. With small amounts it is really useful to transfer satoshis. But you have to write the exact satıshi which you have got in your wallet. Otherwise you will pay transfer fee.