Erin,
I didn't say "odds don't magically change from 1/3 to 1/2 because he offered
a switch", I said "His showing you a door with a booby prize,
which he can always do, does not magically change the odds of your original
pick from 1/3 to 1/2". This is in fact your very reasoning: "they changed
because door number one is no longer an option."
Look at it this way:
Suppose there are 100 doors instead of 3. 99 have booby prizes and you
pick door 57 (because Heinz has 57 flavours :)).
Monty then opens 98 of the doors, each with a booby prize. (He can do this
because he knows what's behind every door.) Only door 66, and your original
choice, door 57, remain closed. He then offers you the opportunity to switch.
By your reasoning, door number 57 has switched from having a 1%
chance to a 50% chance for being the good prize because all those
other doors are no longer an option. That's not sensible. Obviously you
would switch. There's a 99% chance the good prize is behind door 66.
Glenn
Erin Noonan <enoonan@kent.edu> wrote:
>huh?
>odds don't magically change from 1/3 to 1/2 because he offered
>a switch they changed because door number one is no longer an option.
>He offers the switch money after door number one is revealed not before.
>You lost me here Glenn.
>I think Rick is asking if the events are independent. Does
>choice number one affect choice number two. From what I remember
>about coin tosses they are... its doors 2 or 3 thus 50/50 odds
>no magic here just statistics.
>
>Erin
>
>>Hi Rick,
>>Monty doesn't have to offer you money to switch your choice, unless sailing
>>down the river in a boat with Bob P. is not enticing enough. You have a 2/3
>>chance of getting the good prize if you switch, as opposed to 1/3 if you
>>stay with your original choice. His showing you a door with a booby prize,
>>which he can always do, does not magically change the odds of your original
>>pick from 1/3 to 1/2.
>>Glenn
>>
>>"Valence" <valence10@hotmail.com> wrote:
>>
>>>Hey all,
>>>I was hoping that some mathematically/statistically inclined forum member
>might be kind enough to comment on the following "problem'"which has had me
>going 'round in circles for a while:
>>>
>>>Here's the Setup:
>>> Imagine you're a contestant on Let's Make a Deal. Monty Hall calls you
>up to the stage and explains the game to you. He tells you there are three
>doors. Door #1. Door #2. And Door #3. Behind two of the doors (he won't
>tell you which of
>>course) are worthless gag prizes, but behind the third is a valuable prize
>(for this group, we'll imagine it's an unlimited one-on-one Q&A with Robert
>Pirsig as he sails you down the Hudson River on the Arête).
>>> Monty asks you choose a door... you pick door #2. Monty says, "Well
>it's a good thing you didn't pick door#1." Door#1 opens and you see one of
>the gag prizes revealed (let's say... a goat in a wheelbarrow).
>>> Now you're down to your chosen door (door#2) and the remaining door
>(door#3). Monty says, "I'll give you $100 to switch to door#3.... I'll give
>to $200...$300...etc...etc."
>>>
>>>Here's the Question:
>>>Does switching doors improve your odds of winning?
>>>
>>>Here's the Possibilities:
>>>1. Switching won't help. It's a 50/50 chance. Door #2 or Door #3.
> Switching don't mean diddley.
>>>
>>>2. Switching will help. You started with 3 doors. 2 bad and 1 good. Odds
>are, you picked a bad one to begin with. So odds are, if you switch, you're
>switching to a good one.
>>>
>>>
>>>
>>>Can anyone crack this one for me? Does switching improve the odds?
>>>
>>>
>>>thanks,
>>>rick
>>>
>>>
>>>
>>
>>
>>__________________________________________________________________
>>Your favorite stores, helpful shopping tools and great gift ideas. Experience
>the convenience of buying online with Shop@Netscape!
>http://shopnow.netscape.com/
>>
>>Get your own FREE, personal Netscape Mail account today at
>http://webmail.netscape.com/
>>
>>
>>
>>MOQ.ORG - http://www.moq.org
>>Mail Archive - http://alt.venus.co.uk/hypermail/moq_discuss/
>>MD Queries - horse@darkstar.uk.net
>>
>>To unsubscribe from moq_discuss follow the instructions at:
>>http://www.moq.org/md/subscribe.html
>
>
>
>MOQ.ORG - http://www.moq.org
>Mail Archive - http://alt.venus.co.uk/hypermail/moq_discuss/
>MD Queries - horse@darkstar.uk.net
>
>To unsubscribe from moq_discuss follow the instructions at:
>http://www.moq.org/md/subscribe.html
>
>
__________________________________________________________________
Your favorite stores, helpful shopping tools and great gift ideas. Experience the convenience of buying online with Shop@Netscape! http://shopnow.netscape.com/
Get your own FREE, personal Netscape Mail account today at http://webmail.netscape.com/
MOQ.ORG - http://www.moq.org
Mail Archive - http://alt.venus.co.uk/hypermail/moq_discuss/
MD Queries - horse@darkstar.uk.net
To unsubscribe from moq_discuss follow the instructions at:
http://www.moq.org/md/subscribe.html
This archive was generated by hypermail 2b30 : Sat Aug 17 2002 - 16:02:25 BST