No more conversions I see . . . does this mean the 50/50ers are set in their thinking?Originally Posted by Rocket36
If so, one last try:
If you had the choice of sticking with the first choice or switching to both of the other doors, would you switch?
I'm presuming the reader would rather have two chances of winning (67%) instead of just one (33%) and so switch from their original selection to the two other doors. . .
Now consider:
What is the difference between:
- switching to the two closed doors; and
- switching from one door to one of the two other doors when you know for certain which of the two hides a goat?
Does revealing which of the two other doors conceals a goat alter the probability that one of the two door doors will conceal the GTI?
So after the goat is revealed behind one door, there is still a 67% chance that one of these two doors conceals the GTI. And a 33% chance the door we first chose conceals the GTI.
So we get to choose between:
A door with 0% chance of concealing the GTI (the one the host has already opened);
A door with 67% chance (the door we did not first choose);
A door with a 33% chance (the door we chose first).
We already knew one of the doors we did not choose would contain a goat.
Switching to the only other closed door after the first goat is revealed is the same as being allowed to open two doors.
Whether you open both doors at once or Monty helps by first opening one for you makes no difference to the 67% probability that one of these two doors conceals a GTI.
The only question is, are you going to act on this information and have the benefit of effectively opening two doors instead of just one?
Or do you just go with your instinct and stick with your gut feel despite it offering only half the probability if you switched?
You'd kick yourself if you switched and got the goat . . . but twice as often you'd be glad you switched.
Anyone changing their position?
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