I've come across this probability problem and could not solve it. In order to learn, I searched for the solution on the internet and found out that people just printed 1/2. i.e., the answer, no matter the value of n, is always 50%.

Why is that so? I tried making some DP for testing values under ~20 and only when n = 2 the answer is indeed 1/2.

Can someone give me some help on this tough (for me) one?

Appreciate the help!