Monty Hall Problem

[Stacy]

Please can anyone help me with this question.

The Monty Hall problem is named for its similarity to the Let's Make a Deal television

game show hosted by Monty Hall.

The problem is stated as follows. Assume that a room is equipped with three doors.

Behind two are goats, and behind the third is a car.

You are asked to pick a door, and will win whatever is behind it.

Let's say you pick door1. Before the door is opened, however, someone who knows what's behind the doors

(Monty Hall) opens one of the other

two doors, revealing a goat, and asks you if you wish

to change your selection to the third door (i.e., the door which neither you picked nor he

opened).

The Monty Hall problem is deciding whether

you

change your selection or not

that has a better chance of winning the car

.

It’s common sense that if not to change, the

probability of winning is 1/3 but what about changing the selection.

Simulating this game using SAS, for each round, program the fol

lowing,

1)

Assigning two goats and a car to three doors randomly

2)

Picking a door randomly

3)

Picking one of the two remaining doors to open but must showing the goat

4)

Changing the selection to the remaining door

5)

Deciding the result

Repeating these steps for 100

rounds

,

generating a data set including the following five

variables, the round number, the door the car is in, the door chosen initially, the door

chosen after switching,

and

the result(win/lose). Showing the data set and reporting the

frequency

of the initial door chosen, the frequency of the door chosen at the end, the

average rate of winning.

[PaigeMiller]

There are plenty of explanations/solutions of the Monty Hall problem out there on the internet, including Wikipedia.

But it isn't clear why you are posting this in a SAS forum. Are you trying to simulate the results? What is the actual question you are asking?

[Stacy]

I am stuck on writing a code to assign two goats and a car to three doors randomly. I'm just not sure about the right code for this particular one

[PeterClemmensen]

This is a nice starting point.

[PaigeMiller]

While I realize this is a homework problem ... the mathematician in me wants to say that the best and most convincing solution does not involve any simulation at all. This problem can be solved simply by computing probabilities of each event.

[data_null__]

---

@Stacy wrote:

I am stuck on writing a code to assign two goats and a car to three doors randomly. I'm just not sure about the right code for this particular one

---

You could use this code to generate a number of randomizations of the prize.

proc plan ordered seed=89768;
   factors rep=10 door=3 / noprint;
   treatment prize=3 random;
   output out=want prize cvals=('Goat' 'Goat' 'Car');
   run;
   quit;

[Reeza]

IML solution

https://blogs.sas.com/content/iml/2015/04/01/monty-hall.html

Data step approach - Single iteration

http://www.sascommunity.org/wiki/Monty_Hall,_Paul_Erd%C3%B6s,_and_Monte_Carlo

SAS & Python

https://blogs.sas.com/content/sgf/2016/10/12/the-monty-hall-paradox-sas-vs-python/

---

@Stacy wrote:

Please can anyone help me with this question.

The Monty Hall problem is named for its similarity to the Let's Make a Deal television

game show hosted by Monty Hall.

The problem is stated as follows. Assume that a room is equipped with three doors.

Behind two are goats, and behind the third is a car.

You are asked to pick a door, and will win whatever is behind it.

Let's say you pick door1. Before the door is opened, however, someone who knows what's behind the doors

(Monty Hall) opens one of the other

two doors, revealing a goat, and asks you if you wish

to change your selection to the third door (i.e., the door which neither you picked nor he

opened).

The Monty Hall problem is deciding whether

you

change your selection or not

that has a better chance of winning the car

.

It’s common sense that if not to change, the

probability of winning is 1/3 but what about changing the selection.

Simulating this game using SAS, for each round, program the fol

lowing,

1)

Assigning two goats and a car to three doors randomly

2)

Picking a door randomly

3)

Picking one of the two remaining doors to open but must showing the goat

4)

Changing the selection to the remaining door

5)

Deciding the result

Repeating these steps for 100

rounds

,

generating a data set including the following five

variables, the round number, the door the car is in, the door chosen initially, the door

chosen after switching,

and

the result(win/lose). Showing the data set and reporting the

frequency

of the initial door chosen, the frequency of the door chosen at the end, the

average rate of winning.

---