As can be clearly seen from the situation in the question, the previous tosses or flips have no bearing on future tosses or flips. So, no matter how many flips we have done in the past with the counter the next flip will have the probability of getting either an orange or a brown which will be independent of the past events.
As we can see that there are just two possibilities, either we get an orange or a brown. And both of them are equally likely. So the probability of landing on orange side up in any flip is
.
Thus, the probability of landing on orange side up in the 25th flip will be
too.