Today, in my physics class my teacher was talking about how we can never predict the outcome of a coin flip. So I thought: Will the outcome of a coin flip be the same if we do not change the initial conditions (such as launch angle, force position where force is applied,etc.)? Intuitively, I feel that the answer would be yes. But is there something related to quantum mechanics that may produce a different answer?
Today, in my physics class my teacher was talking about how we can never predict the outcome of a coin flip
Your teacher was most likely not talking about this from a QM perspective of how experiments have probabilistic outcomes due to the inherent nature of QM (as we currently understand it).
Your teacher was most likely making a comment about how it is nearly impossible to know all of the relevant initial conditions, system parameters, etc. to accurately predict the result of a coin toss. However, on the spatial and temporal scales a coin toss resides on, it is safe to say we are in the classical mechanics regime. Quantum effects likely play no significant role in any of this. Therefore, you are correct in saying that if we could exactly reproduce the initial conditions of the entire system, then we would most certainly expect the same outcome each time.
In other words, your teacher was talking about inability to predict the outcome based on lack of sufficient information of the system, not because of any underlying quantum mechanical probabilities.
I guess the subject here is chaos, which arises even in classical mechanics, with a very nicely define classical Hamiltonian. "Deterministic chaos" is one of the wonderful oxymorons modern science can produce. In system having exponential dependence to initial conditions, evolution from two "infinitely" close initial states will diverge, and you have a prediction horizon.
If you can reliably predict, say, weather to 3 days and after that all your predictions fail, and you now measure initial conditions 10 times more accurately, you may be able to predict up to 4 days; again 10 times more accurate (100 times from original situation), and you're only able to predict to 5 days. It is likely that you will never be able to predict more than 14 days, whatever precise measures you make.
Flipping a coin raises the same problem.
Edit after discussion in comment section: I'm talking of a coin thrown and landing on a table, which will stabilize after hitting the surface with its edge, bouncing and spinning, which is a chaotic process.