Three closed doors are shown before you. Behind one of these doors is a car; behind the others are "Fish". You do not know where the car is, but the presenter does. You pick a door and presenter opens one of the remaining doors, which doesnot have the car ..
If you have already chosen the correct door, Presenter is equally likely to open either of the two remaining doors with the fish.After presenter has shown a fish behind the door that he opens, you are always given the option to switch doors.
What is the probability of winning the car if you stay with your first choice? What if you decide to switch? Would you prefer to switch doors . Explain .Cheers,
Madhu the monty hall
NB: From next week I will post puzzles on Fridays for you to think over the solution over the weekend . Check for other puzzles from the labels link.
5 comments:
Its better to switch after one of the door opens.
The probability for selecting the correct door, without switching would be 1/6 whereas after switching it rises to 2/6 :-)
I somehow tend to feel the probability of winning if you stick to your door is 0.75, but its not. Its just 0.5. Stay with your current door or choose the other door. Doesn't matter to me.
I am just worried if the car is actually on a wheeled platform behind the door, and the models that come with the car do more than modelling.
The chances of winning by switching or not switching choice are 50:50
---------------------------------------------------------------------
Probability of choosing the correct gate: 1/3
Probability of choosing the in-correct gate: 2/3
if I choose correct gate:
-------------------------
1
-
3
Probability of choosing the correct(With fish) gate by presenter: 1
Probability of choosing the in-correct(With Car)gate by presenter: 0
Not possible since already booked by player
Chance of winning:
1
- X 1
3
if I choose in-correct gate:
-------------------------
2
-
3
now Probability of choosing correct gate(With fish) by presenter: 1/2
now Probability of choosing in-correct gate( With car) by presenter: 1/2
chances of winning if i flip choice
2 1
- X - X 1
3 2
So there are equal chances of winning weather he flips the choice or not.
if we switch to the other door , the probability of winning would be 2/3 and probability of losing would be 1/3...
if we switch to the next door, the probability of winning would be 2/3 and probability of losing would be 1/3
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