June 29, 2010

PUZZLE OF THE DAY

QUESTION - You have reached the final of a game show. You are just one step away from a shiny new car. The host shows you three closed doors. Behind one of these doors is the new car; behind the other two are goats. The host knows which room contains the car.
You are asked to choose a door. After that, the host opens one of the two OTHER doors - one, which he knows, definitely has a goat. Now the host gives you a choice - you can stay with the door you selected or switch to the remaining unopened door by paying 500 rupees. Should you switch? Why?

Solution

Most people (including many mathematics professors at Ivy League colleges) get this one wrong. The instinctive reaction is to not switch, as it will not change the probability of winning - that answer is wrong!

One possible way to explain it is to answer the following questions:

Q: When you first pick a door, are you more likely to pick the car or the goat?
A: The goat. The probability of picking the goat is 2/3.

Q: What is the probability of picking the car?
A: 1/3.

Q: So, is the car more likely to be behind your first choice door or one of the others?
A: One of the others. That probability is 2/3.

Q: If I now eliminate one of the other two doors and give you the option of changing, what should you do?
A: You should switch, as the probability of the car being behind the remaining door is 2/3.



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1 comment:

  1. Interesting Question,
    I had foud a similar question in a hollywood movie 21. So if I go with that movie, I will not swith the door.

    ReplyDelete

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