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Puzzle 6 | (Monty Hall problem)
  • Difficulty Level : Medium
  • Last Updated : 19 Feb, 2021

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?
 

220px-Monty_open_door.svg

Source: http://en.wikipedia.org/wiki/Monty_Hall_problem 

Solution: 
If you switch, you get the car with probability 2/3. So switching is always a good choice. Refer this MIT video lecture for great explanation. Refer online editable Monty hall simulation to play with how things change with multiple doors, prizes etc. 

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
If “the host, who knows what’s behind the doors” opens a door which has a goat, then the probability the car was behind that door was 0 before the door was opened (actually, as soon as the car was placed behind a door). Since the host knows which door has the car behind it, then the probability that the car is behind that door is 1. Hence, the probability of winning by switching is either 0 (if the host knows that door does not have the car behind it) or 1 (if the host knows that door does have the car behind it), not 2/3.

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