Ask Me Help Desk - pool 3,000 people, randomly select 5%, what r odds of being picked each time

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pool 3,000 people, randomly select 5%, what r odds of being picked each time

I have a pool of 3000 people. I need 5% of that pool randomly selected in the result set.

If I run my code, assigning a random number then pulling the Top 5%.

I seem to get some of the same people in the result set each time I run my code.

What is the probability or odds of this happening?

Thank you for any help you can offer.

The probability of getting some of the same people is quite high. The probability of having no duplicates in selecting 60 people out of 3000 is:

$\frac {2940}{3000} \times \frac {2939}{2999} \times \frac {2938}{2998} \times \ ... \ \times \frac {2881}{2941}$

which equals 0.294. So about 70.6% of the time there will be at least one duplicate.

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