Simple Brainteasing problem but 99% solve it wrong (Bayesian interference)

The Monty Hall problem is based on the television game show Let’s Make a Deal. The problem is named after the show’s original host, Monty Hall. The problem was published by Marilyn vos Savant in Parade Magazine. It was also solved by the protagonist of Mark Haddon’s A Curious Incident of the Dog in the Night-Time where he asks: “You are on a game show on television. On this game show the idea is to win a car as a prize. The game show host shows you three doors. He says that there is a car behind one of the doors and there are goats behind the other two doors. He asks you to pick a door. You pick a door but the door is not opened. Then the game show host opens one of the doors you didn’t pick to show a goat (because he knows what is behind the doors). Then he says that you have one final chance to change your mind before the doors are opened and you get a car or a goat. So he asks you if you want to change your mind and pick the other unopened door instead. What should you do?“ Many readers of vos Savant’s column, including scholars holding PhD’s, refused to believe that switching would be to the contestant’s advantage even though it can be demonstrated using proofs and computer simulation. We will use Bayesian inference to show that contestants have a 2/3 chance of winning the car by switching whereas contestants who do not switch only have a 1/3 chance of winning. #simpleProbability #math #Statistics #chances #coinToss #probabilityLine #likelyEvent #unlikelyEvent #NikolaysGeneticsLessons #geetics #pedigree #Genotype #Phenotype #probability #multiplicationRule #additionRule #mutuallyExclusive #IndependentEvents #crashCourse #crashcourse #stats #apStats #apStatistics #conditional #theoretical #empirical #sampleSpace #treeDiagrams #chance #Lesson #maths #data #probabilityFormula #basicProbability #biology #TheMontyHallProblem