On average how many draws does it take to select the winner?

P&AMan

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Sep 15, 2017
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I need to know the average number of draws that it would take before selecting a winning envelope in the following question.

There are 300 envelopes. Only one of the envelopes contains a prize. The other 299 contain nothing. When a losing envelope is drawn, it is then discarded leaving 299, 298, 297, etc total envelopes.

My method was to sum the percentage probabilities of each draw to win until that number exceeded 100%. This would put the number at the 190th draw. Logically, I'm having a tough time wrapping my head around it. Can someone give me a little support on whether or not my method was sound, and if not, what would be the proper method?

Thank you very much.
 

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tkhunny

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Why are you summing?
 
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