Suppose there are 500 people coming to an event that will be giving away 5 door prizes. The 145th person to walk through the doors will get $100, the 219th person will get $50, and the 314th, 315th, and 316th person will get $10. If you and your friends go to the event, but don't necessarily show up at the same time, then what's the probability that at least one of you wins a prize?

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