Actually AsokGreen is correct...but you are also correct
It really depends on the context of the question and situation. Let us take this example:
I flip a coin. I have a 50% chance it is heads. Obviously. No one would dispute that. I decide to flip the coin again. I still have a 50% chance it is heads. Obviously the reason for this is because there are only two possiblities: heads or tails. So in this scenario the question is "What is the chance of getting heads when you flip a coin?".
However, if I were to flip TWO coins at the same time? What would the chance of getting two heads? It wouldn't be 50% because there are more than two possiblities ie: head head, tail tail, head tail, tail head. So the probability is acutally 25% OR 50% times 50%.
So in other words when we are talking about "INDIVIDUAL" events or "SINGLE" events...then yeah...you are right...the probability is always the same. BUT if we talk about multiple simultaneous events then we must factor each probability.
Let use the example of the OP. He plays a game with 8 races. EACH INDIVIDUAL game will always give him 20% chance of getting terran. He restarts and tries again. Still 20%! BUT if he had 8 computers each with GC2 and he simultaneously create a game...then the probability of getting all terrans is 0.16%.
Let us use your example of pregnancy. The chance of a boy is ALWAYS 50% and vice versa for a female. Every pregnancy the chance of a boy is 50%. However, if you had two women and you ask "What is the chance of getting two boys" then that would be 25% because you can either have boy boy, girl girl, boy girl or girl boy ie. 1 in 4.
So in summary: For individual events/scenarios, the probs doesn't change but for multiple or simultaneous events you usually factor in the probs.