I am incredibly frustrated so please excuse me.
I know I can just run the computations but I am struggling to figure out algebraically how I can figure out that n = 23 whereby it takes a minimum of 23 people required for the possibility of 2 people having a birthday on the same day within a year to roughly equal 1/2.
Could someone please help me with this.
I have used the standard notation below which will calculate the given probability of the event not occurring:
$$\frac {1}{2} = \frac{365!}{365^n(365-n)}$$
However I cannot for the life of me figure out how to do the reverse algebraically.
Additionally, I have looked at a number of other forums and I have not found one discussing this aspect.
Thanks