Your question is Rigged Coin Equal Split. Take a moment with it on the right.
Talk me through your thinking if you like. When you're confident, submit your answer and I'll grade it like a real screen (7/10 or better passes).
How would you use a rigged coin that lands heads with probability 0.9 and tails with probability 0.1 to make the chance of choosing either of two movies exactly 0.5?