Editing Birthday problem (section)

=== Number of people with a shared birthday ===
For any one person in a group of ''n'' people the probability that he or she shares his birthday with someone else is <math> q(n-1;d) </math>, as explained above. The expected number of people with a shared (non-unique) birthday can now be calculated easily by multiplying that probability by the number of people (''n''), so it is:
: <math> n\left(1 - \left( \frac{d-1}{d} \right)^{n-1}\right) </math> 
(This multiplication can be done this way because of the linearity of the [[expected value]] of indicator variables). This implies that the expected number of people with a non-shared (unique) birthday is:
: <math> n \left( \frac{d-1}{d} \right)^{n-1} </math> 
Similar formulas can be derived for the expected number of people who share with three, four, etc. other people.