We find the probability of the complement event and subtract from 1.

The complement of this is that all 30 people have different birthdays.

Let's imagine that the people are ordered, say sitting in a row of 30
chairs.  The number of ways we can select 30 birthdays from 365 and
assign them to the 30 ordered people is 365P30.  So that is the
numerator of the desired probability.

The denominator of the probability is 36530, since there
are 365 ways we could assign any birthday to each person. So the
probability of this complement event is

365P30
------
 36530

and this can be calculated with a TI-84 to be .2936837573.  Subtracting
this from 1 we get .7063162427.

So it's better than a 70% probability that 2 or more people among the 30 
have the same birthday.

Edwin