After a successful 25-year career at Goldman Sachs, billionaire investor Leon Cooperman left to start his own hedge fund, Omega Advisors, in 1991.

Today, his firm manages approximately $3.4 billion in assets. But the Wall Street legend wasn't born rich: His parents were working-class Polish immigrants and he grew up in a one-bedroom apartment in the South Bronx.

"Whatever success I've achieved, I think I've achieved it because I've been very lucky, I have common sense and I have a strong work ethic," Cooperman said on CNBC's "Fast Money Halftime Report."

The self-made billionaire is the first to admit that he wouldn't be where he is today without a bit of luck. And he isn't the only successful business titan to do so: His good friend Warren Buffett says the key to his success has been luck, too. Buffett often says he was fortunate to win the "ovarian lottery," meaning that he was born with real advantages that helped him get ahead.