W

Quiz show query

10 Answers
You have three doors in front of you. Behind one door is a great prize worth big money, a luxury car, a world trip etc. Behind the other two doors are booby prizes, worth almost nothing. You make your selection when the quizmaster open one of the other 2 doors revealing a booby prize. You are then asked if you wish to swap your pick to improve your chances. Do you sit with your initial choice of door or do you swap for the other door, or does it make no difference?
S

This is getting really intresting.

I have met a very few persons like you.

Your type are totally convinced of their own logic and rarely introspect.

Let me make one more try ....

In this 10 door case initailly you had to make a choice from ten doors so had the probability to be 1 /10. Agreed.

Now once you open 8 doors and all of them are booby prizes you know for sure that one of the two is prize and one is not.As the 8 doors are opened and results are already known they dont come in the picture at all.
These doors now have to be completely ignored and as the choice has to be only made from the two remaining doors the probability is 1/2 i.e 50 %.(Two because though i have made a selection the result is not yet known and my choice can be wrong or right and so it can be with the other remaining door ).

We have to consider both the remaining doors because my selection could as well been for the other unopened door.

Two doors represent two distinct unique combinations out of which one is to be selected(8 others are already out of reckoning).

That is the reason why the choice again boils to 1 / 2.

Hope you will understand and reconsider your opinion else please consult a mathematicain.

...
S

Hi Wristb34

Let me illustrate.

Let the three doors be A,B and C.
Let A contain money
Let B and C contain booby prizes.

The quizmaster opens a door with a booby prize which is either B or C, say it is B.
Now what are my chances ?

1 - If I had selected A then my chance of winning would be 50-50 i.e one of two available combinations.Luckily I choose the right one.

2 - If I had selected C then my chance of winning would be 50-50 i.e one of two available combinations.UnLuckily I choose the wrong one.

The fact that the quiz master reveals one of the three doors improved my chances of winning by reducing the odds from 1/3 to 1/2.

This is a purely mathematical solution.
Hope you agree .

If you think this is not right , I would advise you to sit down with a paper and pencil and list out all possible unique combinations of the remaining two doors, and you will find what I am saying is correct.

...
S

Hi Wristb34

Out of the three doors one has been opened and it has a booby trap.
Hence there are only two doors left , one with a booby trap and one with grand prize.

Now the probability that you will win grand prize is 1/2 = 50 %.
So even when you swap them the probability of winning is going to remain the same,hence whether you will win a grand prize or not is entirely based on chance or call it luck.

Now whether to swap it or not depends upon the person's individual choice.If he is not confident enough with what he choose first then he may opt for the second one .. but eventually it makes no difference at all as its entirely based on luck.

...
W

I am being unfair as I know the answer to my own question which caused a furore in the circles of mathematicians and logicians a few years ago. It seems to be as you say but it is not.

Consider a more extreme case say 10 doors with one grand prize and 9 booby prizes. You make your pick and the quizmaster opens 8 doors with booby prizes leaving just 2 doors. One of them must be the grand prize and one is clearly not. Your door has a 1/10 chance of winning. Opening the 8 doors has not changed this. How could it? So the other door now has a 9/10 chance and you swap of course. Try it with a deck of cards.
...

W

As I said there was a furore and we are seeing one again in miniature. Please be assured I am right because I know the answer and I knew I would get this sort of response. It is mean of me to do this as many people and clever ones too such as your goodself, are convinced they are right. As I say use a deck of cards and you will be convinced.

In absolute goodwill I assure you, Wristb34 ...

W

I cannot claim the right answer myself but I can point anyone who cares to look at the full-blown controversy that erupted when Marilyn vos Savant gave her solution. It makes for an enlightening read. See
http://www.marilynvossavant.com/articles/gameshow.html
Chances of winning improve from 1/3 to 2/3 when you swap and anyone can confirm this by experiment if they want to.

...
W

If you stick with your initial pick then the chances of winning the big prize remain at 1/3. It does not matter if the quizmaster opens the door to one of the booby prizes, your chances were fixed when you made your initial choice. Now if you swap, your chances improve from 1/3 to 1/2. ...

S

Hi,

Its pretty simple once the initail conditions are changed the probability has to be recalculated.You better consult a maths teacher so that you can understand what I am trying to covey.

...
M

I would take ther orther doors for something that was woth something because u could get something out of it

...
W

That's what most people think but it is not right.

...