Request: Probability Calculation

If he used the numeric approximation formula from the bithday page for the calculation maybe there is some error in 30K


This is incorrect, because you have to consider every combination of two people within the pool. Have a look at the Birthday problem for a similar example of where your intuition is wrong.
{\displaystyle {\begin{aligned}p(n,d)&\approx 1-e^{-{\frac {n(n-1)}{2d}}}\\[6pt]&\approx 1-e^{-{\frac {n^{2}}{2d}}}.\end{aligned}}}



even on that link it says
The following table shows the probability for some other values of n (for this table, the existence of leap years is ignored, and each birthday is assumed to be equally likely):
300 (100 − 6×10−80)%
350 (100 − 3×10−129)%
365 (100 − 1.45×10−155)%
≥ 366 100%
[td]
[/td]​
would you bet the house on 366 people in a room having no shared birthday. ?
eg. being born later in the year and being older in school year is meant to be advantageous for qualifications , so a room full of 366 graduates might, for example, be biassed
 
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