A seemingly counterintuitive problem in probability that gets its name from the TV game show, ‘Let’s Make a Deal’ hosted by Monty Hall. On the show a participant is shown three doors behind one of which is a valuable prize and behind the other two booby prizes. The participant selects a door and then, before the chosen door is opened, the host opens one the two remaining doors to reveal one of the booby prizes. The participant is then asked if he/she would like to stay with the originally selected door or switch to the other, as yet, unopened door. Many people think that switching doors makes no difference to the probability of winning the valuable prize but many people are wrong because switching doubles this probability from a third to two thirds.
Monty Hallproblem
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