how many people do u think need 2 b in a room before there is a 50/50 chance that 2 of them will have the same birthday????????
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In probability theory, the birthday problem or birthday paradox pertains to the probability that in a set of randomly chosen people some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 366 (excluding February 29 births). But perhaps counter-intuitively, 99% probability is reached with just 57 people, and 50% probability with 23 people.
The following table shows the probability for some other values of n
.n............p ( n )
10..........11.7%
20..........41.1%
23..........50.7%
30..........70.6%
50..........97.0%
57..........99.0%
100........99.99997%
200........99.999999999999999999999999…
300........(100 − (6×10−80))%
350........(100 − (3×10−129))%
366........100%
The following table shows the probability for some other values of n
.n............p ( n )
10..........11.7%
20..........41.1%
23..........50.7%
30..........70.6%
50..........97.0%
57..........99.0%
100........99.99997%
200........99.999999999999999999999999…
300........(100 − (6×10−80))%
350........(100 − (3×10−129))%
366........100%
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23..
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366.