**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.**

*QUESTION -*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?*

**The goat. The probability of picking the goat is 2/3.**

*A:*

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

*A:*

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

*A:*

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

*A:*
Interesting Question,

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