I read all the time that you can't mine bitcoin on your home computer. In a sense they are right, however mining other cryptocurrencies such as Monero (XMR) and then being paid in Bitcoin is a real possibility.
More about Monero (XMR) for mining
Monero (XMR) is a popular anonymous digital currency
Monero (XMR) is well-suited for mining with a home computer
The miner that supports Monero but pays in Bitcoin is CryptoTab