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I was at a party where there was a lucky draw. There were about 200 people and each of them had put a chit with their name on it, in a transparent bowl. There were 10 prizes. The announcer chose a person at random to pick a chit for each prize. For one of the prizes, the picker picked his own chit ( there was no hanky-panky). Some one said what are the chances of that happening.

Now I am trying to calculate the chances of such a thing happening. Each chit had a 0.5% chance of being picked. If we also assume that the announcer selected the picker randomly (0.5% chance of getting selected to pick) . Then the chance of a picker picking his own chit = 0.5% * 0.5% = 0.0025%

1. Is the answer correct?

2. My interpretation of how likely is such an event: As likely as any random event out there. I think we can’t use the 0.0025% probability figure here because we know that this experiment will not be carried out hundreds of times. The calculated figure is meaningful only if we repeat the experiment many times. Is that a correct interpretation?

3. If the announcer had pre-determined the pickers, would the chance of such an incident go to 0.5%?

Thanks.

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# Interpretation of a rare event - lucky draw

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