Editing Birthday problem (section)

===Same birthday as you===
[[Image:Birthday paradox.svg|thumb|right|upright=1.4|Comparing {{math|''p''(''n'')}} = probability of a birthday match with {{math|''q''(''n'')}} = probability of matching ''your'' birthday]]
In the birthday problem, neither of the two people is chosen in advance. By contrast, the probability {{math|''q''(''n'')}} that ''at least one other person'' in a room of {{mvar|n}} other people has the same birthday as a ''particular'' person (for example, you) is given by

: <math> q(n) = 1 - \left( \frac{365-1}{365} \right)^n </math>
and for general {{mvar|d}} by
: <math> q(n;d) = 1 - \left( \frac{d-1}{d} \right)^n. </math>

In the standard case of {{math|''d'' {{=}} 365}}, substituting {{math|''n'' {{=}} 23}} gives about 6.1%, which is less than 1 chance in 16.  For a greater than 50% chance that ''at least'' one other person in a roomful of {{mvar|n}} people has the same birthday as ''you'', {{mvar|n}} would need to be at least 253. This number is significantly higher than {{math|{{sfrac|365|2}} {{=}} 182.5}}: the reason is that it is likely that there are some birthday matches among the other people in the room.