Over the years, one fact has been very subtly revealed to me by chance. That fact is..that there will always be a finite probability that I do not understand probability. That was recently underscored by my chance encounter with the Monty Hall Paradox, a seemingly obvious problem with a not so obvious solution. For folks who have come across this and still have a niggling doubt about it, I have laid out all the permutations in the below diagram along with the associated explanation. Needless to say, I had to do this to convince my self first of all.
Prerequisites for reading further:
1) What is the Monty Hall Paradox? Why on Earth do we have wikipedia? Please go here -> Monty Hall
2) An interest in Mathematics and/or
3) Extreme Boredom :-)
Ok, since you are already here, lets get to the solution. Here are the scenarios
Explanation:
Lets take the first three rows from the above snapshot. Here, the prize is behind the first door and the three rows list out the three possible choices that the player can make.
The player's choice is mentioned under the "Original Choice" column.
The next column shows the final outcome provided the player decides not to switch while the subsequent column shows the result in case he had decided to switch.
Taking the second row as an example, the prize is behind Door 1, the player chooses Door 2, the host then opens Door 3. The player has the option of sticking with his original choice (Door 2) and lose or switch to the only other remaining door i.e Door 1 and consequently win.
The overall success probability for all the scenarios is listed below and as counter intuitive as it may seem at first, the results speak for themselves.
The life lessons I gathered from this are
1) Your first choice is likely to be the wrong one
2) If you get the chance - Switch :-D
Prerequisites for reading further:
1) What is the Monty Hall Paradox? Why on Earth do we have wikipedia? Please go here -> Monty Hall
2) An interest in Mathematics and/or
3) Extreme Boredom :-)
Ok, since you are already here, lets get to the solution. Here are the scenarios
Explanation:
Lets take the first three rows from the above snapshot. Here, the prize is behind the first door and the three rows list out the three possible choices that the player can make.
The player's choice is mentioned under the "Original Choice" column.
The next column shows the final outcome provided the player decides not to switch while the subsequent column shows the result in case he had decided to switch.
Taking the second row as an example, the prize is behind Door 1, the player chooses Door 2, the host then opens Door 3. The player has the option of sticking with his original choice (Door 2) and lose or switch to the only other remaining door i.e Door 1 and consequently win.
The overall success probability for all the scenarios is listed below and as counter intuitive as it may seem at first, the results speak for themselves.
The life lessons I gathered from this are
1) Your first choice is likely to be the wrong one
2) If you get the chance - Switch :-D
