>>132898116>Why is the Monty Hall problem so popular? It's just a simple exercise in probability.It really has to do with psychology AND people doing math wrong.
Simply put in reality people ALWAYS chose to "stay" with their choice in the Monty hall scenario. They're making the assumption that it's a 1/3 chance to chose the right one. all opening one of the other two doors does is prove that they might have chosen the "right" door.
However the math and reality actually shows that they're almost always better changing their pick; the reason?
before the door is chosen they have a 1/3 chance to chose the right door, which means there is a 2/3 chance the "right" door is one of the two they didn't chose.
when one of the two doors they didn't chose is opened and shown to be empty, they mistakenly think the odds have become 50/50, and see no reason to change their choice.
HOWEVER in reality the "other" door STILL has a 2/3 chance to be the right door, which is better then the 1/3 chance with the door they chose. The original odds that it's one of the other two doors remains the same even though you opened an empty door. so choosing to CHANGE your choice will be right x2 more often then staying with your current choice.
The thing of it is, people are rather good with simple fractions and the concept of basic gambling "chance" they just suck at PROBABILITY. And the Monty Hall paradox exploits the rules of probability and people's general understanding of "chance" to contrive a scenario where almost EVERYONE will chose the "wrong door" and think they made the "right" choice (by staying put).
