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


LisaMK1957
Oct 10, 2013, 06:38 AM
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.

ebaines
Oct 10, 2013, 08:21 AM
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.