Monty Hall problem- Is it worth changing your mind?

Discrete Mathematics Level pending

Monty Hall used to host a program called "Let's Make A Deal" and one of the "deals" went as follows. You are shown 3 doors and are told that behind one door is a new car yet behind each of the other doors is a gag prize - a goat. You make your pick then Monty Hall opens a door you haven't chosen and shows that behind it is a goat. He then asks you if you want to change your selection. Should you change your mind, stick with your original choice or does it really matter?

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