Forums / Miscellaneous Discussions / Help me Understand the Monty hall problem

Help me Understand the Monty hall problem
22:59:32 Sep 18th 22 - Lady Jasmina:

Seen this in two movies already

Situation:

There are three doors
Door A, Door B and Door C
Behind only one door is a car

You pick Door A 
Host who knows where the car is opens Door C, its empty
Offers you to change if you want
What do you do?

So first you have 33.33% chance to guess right
After Door C is opened it means you have 50% chance
But in movies they say now you have 66% if you change!

But how? Why?
Why is it not 50%
The genius in movie says I switch cause its 66% now
Could someone explain why is it better to switch to B

I am thinking I had 33% first and now 50%
Switching gives me 66%? 
Explain please


23:05:15 Sep 18th 22 - Lady Jasmina:

23:17:32 Sep 18th 22 - Jarl Ivar The Boneless:

Because you had 3 choices. 33.3 per leaves you with a 66.6 choice with either one you pick.


23:24:38 Sep 18th 22 - Phat (Grand Moff Thrawn):

@jarl, not quite. 



This is called the Monty hall problem. 

Best explained when using larger numbers. 

Letís say I had 100 boxes. One had 100 bucks and the rest had nothing. If you picked the correct box you get to keep the 100 bucks. 


So you pick box #32. 
I open boxes 1-31, 33-67, and 69-100. Theyíre all empty. 

You can now pick to keep #32 or switch #68. Would you switch to 68?


I would. You picked #32 and it was only a 1% chance. You can now pick 68 for a 99% chance instead(the sum of the others that weíre limited, plus itís odds)


23:38:23 Sep 18th 22 - Jarl Ivar The Boneless:


Phat:

@jarl, not quite. 



This is called the Monty hall problem. 

Best explained when using larger numbers. 

Letís say I had 100 boxes. One had 100 bucks and the rest had nothing. If you picked the correct box you get to keep the 100 bucks. 


So you pick box #32. 
I open boxes 1-31, 33-67, and 69-100. Theyíre all empty. 

You can now pick to keep #32 or switch #68. Would you switch to 68?


I would. You picked #32 and it was only a 1% chance. You can now pick 68 for a 99% chance instead(the sum of the others that weíre limited, plus itís odds)


You're less lazy than myself lol I knew someone would explain it in detail.


23:54:50 Sep 18th 22 - Percy (Sir Percy The Arma Caster):

This is fundamentally why I hate probabilities. A given chance relative to the start Vs chance relative to the current conditions.


In both Jasminaís and Moffís cases, the end result is a 50/50 shot looking at purely the choices presented before you. But by removing the past cases, youíve cleared 33% (in Jasís case) and 98% (in Moffís case) of the options, leaving you with the remainder.

Just like any good problem, itís all about framing :) in application, itís a 50/50 in the current situation, though relative to the options being cleared, itís a higher chance. But for the point of final decision, itís 50/50.

I hate probabilities with a passion, cause they can be severely misleading.


00:22:41 Sep 19th 22 - Matthew (Chief Trogdar):

BUMP LOL


00:43:04 Sep 19th 22 - Phat (Mr. Grimfuggah):

Thanks for speaking to that @percy, I believe the actual proofs behind it would argue each selection is isolated from the others. So when itís 2 choices, itís 50%


16:59:03 Sep 19th 22 - Matthew (Chief Trogdar):

You guys are all so stupid, are you telling me that there's nobody guarding the doors?
Is there no way to use sound or senses to infer which door the car is behind?


Can't you judge the way the HOST reacts (guy guarding the doors) to know which door it's behind?

There is no way this one is 50/50 unless you're as dumb and dishonest as a scientist.

You can be autistic and its still at least 51/49 if you have any sense at all about how the host reacts when you solicit a door

Consider it like 'Poker'


11:26:23 Dec 21st 22 - Princess Yasmina:

Help me understand part II



You play lottery(1-60). Random numbers; you chose 1,11,22,33,44,55
Is the chance of winning the same if you took any other random numbers?
If you take 1,2,3,4,5,6 would it have the same chance of winning?
Could someone explain?


12:58:14 Dec 21st 22 - Random (Duke Random):

Yes, you have the same 1/x chance of winning regardless of which numbers you pick.

think of this on a smaller scale

you pick a number 1 or 2. Whichever number you pick you have a 50% chance of winning.

Same applies here just on a larger scale, statistically you have the same chances to win.


16:37:15 Dec 21st 22 - Ms. Jasmine:

If you do 1 million rolls, and see the outcome. You're saying that once you add up all the million outcomes that came out, you will have approx the same amount of times that 1,2,3,4,5,6 will apear as numbers 11,22,33,44,55,66, right?


18:39:39 Dec 21st 22 - Random (Mr. Gods Big Spoon):

Well considering most lottery's are 1/100million or so, i'd say that you'd either see each sequence 0 or 1 time with 1million rolls.

But theoretically - given enough random rolls - you'd see a pretty similar distribution.

However that doesn't mean after your number not being rolled you're more likely to have it come up - it's still the same chance to hit every time. Theoretically - the same set of numbers can roll repeatedly forever.


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