Monty Hall Twister
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 where a and b are coprime positive integers. What is a+b?
The answer is 11.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
There is a 4 1 chance that Felix made the right choice initially. This means a 4 3 chance that Felix's initial choice was wrong which means he should switch. Even so, this does not guarantee that he will finally choose the correct door as he still has to choose between two doors. However, assuming Felix's initial choice was wrong, he will have a 1 in 2 chance of finally choosing the correct door. The overall possibility of Felix choosing the right door after switching is 4 3 * 2 1 = 8 3 which is still higher than the 1 in 4 chance if Felix's does not switch.
The answer is 3+8=11.