Partying with Bill Gates...and a Coin-Toss Quandary

The Puzzler

RAY: A fellow finds himself at a party at, of all places, Bill Gates' house. And, who should be standing next to him but Bill Gates himself! The fellow says, "Gee, this is a pretty big living room you have. It's jam-packed with people."
Gates says, "How many people do you think are here?"
The fellow says, "I don't know. Maybe about 1100?"
Gates replies, "That's very good. There are about 1100 people here. You're very good with numbers. Are you into games of chance? If we flipped a coin 10 times in a row, do you think there's anyone in this room who could call it correctly each time?"
The fellow says, "I suppose there's a chance, but it's got to be a pretty small chance."
And Gates says, "I think there is a chance. In fact, I'll bet you $10 million to your $1,000 that it can happen in this room, that there's one person who could guess it correctly 10 times in a row."
The guy says, "You're on, Gates."
Should he have taken the bet? What do you think?

Think you know? Drop Ray a note!

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