One day, Brenda’s boyfriend, Felix, visited her house to date with her. Felix encountered four doors. Brenda’s father, Mr Tan, explained that Brenda has two elder brothers (Charles and Darius) and a younger brother Alfred.

Each of the four siblings was behind one of the four doors. Felix could only date with Brenda if he could open the door with Brenda behind. But if Felix chose a door with Charles, Darius or Alfred behind, he would go home crestfallen.

Felix then made his choice. Mr Tan then opened one of the other three doors and out came Alfred. Mr Tan then asked Felix, "Do you want to stick to your original choice or switch to one of the two remaining doors?"

Assuming Felix made the best strategy, his chances of arriving at the correct door is \(\frac{a}{b}\) where a and b are coprime positive integers. What is a+b?

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