Three Curtains

  • Christian Chat is a moderated online Christian community allowing Christians around the world to fellowship with each other in real time chat via webcam, voice, and text, with the Christian Chat app. You can also start or participate in a Bible-based discussion here in the Christian Chat Forums, where members can also share with each other their own videos, pictures, or favorite Christian music.

    If you are a Christian and need encouragement and fellowship, we're here for you! If you are not a Christian but interested in knowing more about Jesus our Lord, you're also welcome! Want to know what the Bible says, and how you can apply it to your life? Join us!

    To make new Christian friends now around the world, click here to join Christian Chat.
R

rstrats

Senior Member
#1
Aug 28, 2011
744
43
28
#1
You are a contestant on a game show. There are three curtains. Behind one of the curtains is a new car. You are asked to choose one of the curtains. Lets say that you choose curtain #1. The host of the show - who knows where the car is so as not to end the game prematurely - opens curtain #3 and there is no car behind it. The host now gives you a choice. You can stay with curtain #1 or you can change your choice to curtain #2. The question now is: would it be to your advantage to stay with curtain #1, or would it be to your advantage to change to curtain #2 or would there be no advantage either way?
 
Lynx

Lynx

Folksy yet erudite
#2
Aug 13, 2014
27,413
9,401
113
#2
It would be to my advantage to boycott this game show. I don't need a new car and I don't want to get stuck paying taxes and insurance on it.

But if you want the car, you have a 50/50 shot either way.
 
tourist

tourist

Senior Member
#3
Mar 13, 2014
42,598
17,062
113
69
Tennessee
#3
Lynx said:
It would be to my advantage to boycott this game show. I don't need a new car and I don't want to get stuck paying taxes and insurance on it.

But if you want the car, you have a 50/50 shot either way.
Click to expand...
Ergo. No, the car behind the curtain is a Yugo. Your first impression about the boycott was the correct choice.
 
Genipher

Genipher

Well-known member
#4
Jan 6, 2019
2,285
1,688
113
#4
Wasn't this a real game show once upon a time? 🤔
 
R

rstrats

Senior Member
#6
Aug 28, 2011
744
43
28
#6
Lynx said:
,,,you have a 50/50 shot either way.
Click to expand...
What would you do if after your pick of curtain #1, and before any curtains were opened, the host told you that you could change your pick to both curtains #2 and #3?
 
Lynx

Lynx

Folksy yet erudite
#7
Aug 13, 2014
27,413
9,401
113
#7
rstrats said:
What would you do if after your pick of curtain #1, and before any curtains were opened, the host told you that you could change your pick to both curtains #2 and #3?
Click to expand...
Without knowing what's behind any of the curtains, that would change your odds to two out of three that you get the car. It would be better to pick two and three than stay with one.

I'm still trying to guess where you are going with this stuff. Can you give us a hint?
 
R

rstrats

Senior Member
#9
Aug 28, 2011
744
43
28
#9
Lynx,
re: "It would be better to pick two and three than stay with one."

What do you know about curtains #2 and #3? You know that at least one of them doesn't have a car behind it. But you say you would switch anyway. Which means that you get to open both curtains #2 and #3. So what is the difference if you open both of them or the host opens one of them for you?

re: "I'm still trying to guess where you are going with this stuff."

It's just a logic problem. I'm not going anywhere with it.
 
Lynx

Lynx

Folksy yet erudite
#10
Aug 13, 2014
27,413
9,401
113
#10
rstrats said:
So what is the difference if you open both of them or the host opens one of them for you?
Click to expand...
If all three are unknown, the probability of any curtain having the car is one third. If you stay with one, you have a one third chance. If you switch to two AND three, you have a two thirds chance.

If the host already opened three, each of the two remaining curtains has a one in two chance.
 
R

rstrats

Senior Member
#11
Aug 28, 2011
744
43
28
#11
[QUOTE="Lynx, post: 4598148, member: 203470"

If the host already opened three, each of the two remaining curtains has a one in two chance.[/QUOTE]


You can look at it this way: Think of it as two areas. Area "A" contains curtain #1 and area "B" contains curtains #2 and #3. There is a 1/3rd chance that the car is in area "A" and a 2/3rds chance that it is in area "B". Before opening any curtains, you KNOW that at least one of the curtains in area "B" doesn't have the car behind it. So by the host knowingly opening a curtain in area "B" that doesn't have a car behind it doesn't change the 2/3rds odds that area "B" still has a car in it. So it is to your advantage to switch to area "B".
 
Lynx

Lynx

Folksy yet erudite
#12
Aug 13, 2014
27,413
9,401
113
#12
Not at all. When the host opens #3, it changes the probability of the remaining curtains. Your area B now has a 50/50 chance, not a two thirds chance.
 
Lynx

Lynx

Folksy yet erudite
#15
Aug 13, 2014
27,413
9,401
113
#15
rstrats said:
Maybe you'll see why you're wrong if you go to the below link.

https://www.mathwarehouse.com/monty-hall-simulation-online/
Click to expand...
I ran it three times... and got a car three times. I think that program is rigged. :p

Still doesn't change simple math though. If one door has been opened, there are two doors left. If there is a car behind one door and there are two doors, the probability of the car being behind a given door is 50% no matter what.
 
R

rstrats

Senior Member
#16
Aug 28, 2011
744
43
28
#16
[QUOTE="Lynx, post: 4598161, member: 203470 When the host opens #3, it changes the probability of the remaining curtains. Your area B now has a 50/50 chance, not a two thirds chance.[/QUOTE]

Area "B" contains curtain 2 and curtain 3 which means that there is a 2/3rds chance that the car is in area "B".
You know that at least one of the curtains in area "B" doesn't have the car behind it.
So how is knowing that it isn't behind curtain 3 change the odds that the car is still in area "B"? The only thing that changes is the odds that it is behind curtain 3 which goes from 1/3rd to Zero.
 
Lynx

Lynx

Folksy yet erudite
#17
Aug 13, 2014
27,413
9,401
113
#17
Those odds go somewhere though. They don't just disappear. Specifically, half the odds go to each of the remaining doors.
 
R

rstrats

Senior Member
#18
Aug 28, 2011
744
43
28
#18
Lynx said:
Those odds go somewhere though. They don't just disappear.
Click to expand...
That is correct. They go to curtain #2, the remaining curtain in area "B" which has a 2/3rds chance of containing the car.
 
Lynx

Lynx

Folksy yet erudite
#19
Aug 13, 2014
27,413
9,401
113
#19
If you want to play it that way, go ahead and have fun. Hope you like goat milk.

Actually I'll take the goat you win. (Do they ever actually give people the goat? Or is it just the "you lose" symbol that they keep and reuse?) I like goat milk. I make homemade boiled custard out of it.
 
Genipher

Genipher

Well-known member
#20
Jan 6, 2019
2,285
1,688
113
#20
Lynx said:
If you want to play it that way, go ahead and have fun. Hope you like goat milk.

Actually I'll take the goat you win. (Do they ever actually give people the goat? Or is it just the "you lose" symbol that they keep and reuse?) I like goat milk. I make homemade boiled custard out of it.
Click to expand...
I'd rather a goat than a car, too. :)
 
You must log in or register to reply here.