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        riddles >> medium >> Bummer Train Ride (JP05)
        
(Message started by: FiBsTeR on Oct 11th, 2007, 3:28pm)
Title: Bummer Train Ride (JP05)
Post by FiBsTeR on Oct 11th, 2007, 3:28pm
==ORIGINAL PROBLEM (post deleted)==
You and your sister are caught on board a train without a ticket. The conductor decides to punish you by offering the two of you a box of what appear to be nine identical chocolates, three of which are filled with poison. You each eat one in turn; you decide to go first, and your sister will go second.
(i) What is the probability that you survive?
(ii) What is the probability that your sister will survive if you survive?
(iii) What is the probability that your sister will survive if you die?
(iv) Should you convince your sister to go first instead?
(v) What is the probability that you survived if your sister survived?

Credit: JP05
--------------------------------



When does the "game" end?
Title: Re: Bummer Train Ride
Post by JiNbOtAk on Oct 11th, 2007, 6:08pm
I'm confused, how many times do we need to choose ? Only once ? Or until all the chocolates are finished ( which makes the probability of either one dying = 1 )
Title: Re: Bummer Train Ride
Post by FiBsTeR on Oct 11th, 2007, 7:50pm
Let me clarify what I meant (and what JiNbOtAk meant I believe):

When I asked when the game ends, I meant how many times does each person choose a chocolate (only once, or until one person dies -- which is maybe what you wanted, like Russian Roulette (http://en.wikipedia.org/wiki/Russian_Roulette)?, or until the chocolates are gone -- trivial); these are all different "games":

If you are saying each person only needs to choose once, the answers become:

(i) the probability of surviving going first is 2/3
(ii) the probability of surviving going second given that the first has survived is 5/8 (the probability of surviving going second in general is also 2/3)
(iii) the probability of surviving going second if the first has died is 3/4
(iv) doesn't matter; the probability of surviving is equal either way
(v) if your sister survived going second, then the probability that you survived going first is 5/6 (i think)

If you are saying each person picks until one person dies, I think the answers are:

(i) 17/42
(ii) 11/28
(iii) 1 (if you die, your sister lives)
(iv) if you like your sister, have her go second; otherwise, have her go first
(v) 0 (if your sister survives, you die)

If you are saying each person picks until all the chocolates are gone:

(i) 0 (you die)
(ii) not defined
(iii) 0 (muerto)
(iv) doesn't matter, you both die
(v) not defined
Title: Re: Bummer Train Ride
Post by JiNbOtAk on Oct 11th, 2007, 8:04pm

on 10/11/07 at 19:50:45, FiBsTeR wrote:
Let me clarify what I meant (and what JiNbOtAk meant I believe):

When I asked when the game ends, I meant how many times does each person choose a chocolate (only once, or until one person dies -- which is maybe what you wanted, like Russian Roulette (http://en.wikipedia.org/wiki/Russian_Roulette)?, or until the chocolates are gone -- trivial); these are all different "games":


Yup, that's what I meant to clarify too.


on 10/11/07 at 19:50:45, FiBsTeR wrote:
(iv) doesn't matter; the probability of surviving is equal either way


Really ? Never mind..  :-/


on 10/11/07 at 19:50:45, FiBsTeR wrote:
(iv) if you like your sister, have her go second; otherwise, have her go first


This is due to the total quantity,irregardless of the probability, right ?
Title: Re: Bummer Train Ride
Post by FiBsTeR on Oct 11th, 2007, 8:09pm

on 10/11/07 at 20:01:58, JP05 wrote:
I don;'t want any of your cheap remarks or your attitude in any of my stuff.


???

I'm not sure what cheap remarks or attitude you are referring to... I provided three different interpretations to your problem and answered the questions for each interpretation.

Referring to the one you quoted, (i) the probability of living in a game where you must eat a poisoned chocolate is 0 (hence why I said you die, because you must eat a poisoned chocolate), (ii) you cannot survive this game, so the probability does not exist (i mentioned srn347 because his posts often involved operating with things that did not exist), (iii) muerto means dead if I remember correctly, and the probability of your sister surviving is 0, (iv) the probability of surviving in this game is 0 either way, so it doesn't matter when your sister chooses, (v) again, your sister cannot survive this game since she must eventually eat a poisoned chocolate.

I don't know what you found offensive in any of my posts, really...


on 10/11/07 at 20:01:58, JP05 wrote:
you are a ********* problem yourself and you just might as well be the coward you spoke of.


I don't ever remember mentioning cowards...ever...at all in this whole forum...
Title: Re: Bummer Train Ride
Post by FiBsTeR on Oct 11th, 2007, 8:15pm

on 10/11/07 at 19:50:45, FiBsTeR wrote:
If you are saying each person only needs to choose once, the answers become:

[...]

(iv) doesn't matter; the probability of surviving is equal either way



on 10/11/07 at 20:04:14, JiNbOtAk wrote:
Really ?


If you go first, there are 9 chocolates, 6 of which are safe, so the probability of surviving is 6/9 = 2/3.

If you go second, there are two possibile situations: the first survives (2/3), and you survive (5/8), or the first dies (1/3), and you survive (3/4). Thus the probability of surviving is (2/3)(5/8) + (1/3)(3/4) = 2/3.

The two probabilities are equal, so it doesn't matter whether you go first or not.



EDIT: JP05, I apologize if the reference to srn347 offended you, and I will gladly edit it.
Title: Re: Bummer Train Ride
Post by JiNbOtAk on Oct 11th, 2007, 8:24pm
Whoa JP05, calm down. FiBsTeR's just seeking clarification for your question. You have to admit, some point of it is a bit vague. And he did provide answers for all different cases. Maybe I'm missing something, but I did not see any offensive remarks in his posts.

As for the srn347 remark, maybe you didn't get it, but it was sorta of srn347's trademark, to discuss undefined concepts ( 0/0 being his personal favourite ).


Quote:
ii. if you choose first and survive, what is the probability that your sister survives?

For cases where the game ends only when the chocolates are finished, then this statement is irrelevant, as both of you would die from eating a poisoned chocolate. ( In fact, you won't be able to finish all chocolates, both of you would definitely die by the eight one.  )

Added :


on 10/11/07 at 20:15:14, FiBsTeR wrote:
If you go first, there are 9 chocolates, 6 of which are safe, so the probability of surviving is 6/9 = 2/3.

If you go second, there are two possibile situations: the first survives (2/3), and you survive (5/8), or the first dies (1/3), and you survive (3/4). Thus the probability of surviving is (2/3)(5/8) + (1/3)(3/4) = 2/3.

The two probabilities are equal, so it doesn't matter whether you go first or not.


Yeah, I came to the same conclusion right after I posted my response.  :P
Title: Re: Bummer Train Ride
Post by FiBsTeR on Oct 11th, 2007, 8:32pm
I'm very interested in what the probabilities would be in the case where they each eat until one dies; my probability is very weak, so I mostly rely on tree diagrams and intuition, which leaves a lot of room for error.  :P
Title: Re: Bummer Train Ride
Post by ima1trkpny on Oct 12th, 2007, 7:57am
Wow... it looks JPO5 must have gotten really really mad... cause she deleted her account... 0.0
I don't understand why she got so upset...  :-/
Title: Re: Bummer Train Ride
Post by Ghost Sniper on Oct 12th, 2007, 8:11am
Are you sure that JP05 didn't just get banned?
Title: Re: Bummer Train Ride
Post by ima1trkpny on Oct 12th, 2007, 8:22am

on 10/12/07 at 08:11:54, Ghost Sniper wrote:
Are you sure that JP05 didn't just get banned?


That may be... she did throw a temper fit... but at least what I saw wasn't srn level irritating... just like she misinterpreted and overreacted. My guess would have been that there would have been at least 1 mod. warning...
Title: Re: Bummer Train Ride
Post by Ghost Sniper on Oct 12th, 2007, 9:00am
If srn is gone, then that means I'm the youngest one on this forum.  :P
Title: Re: Bummer Train Ride
Post by FiBsTeR on Oct 12th, 2007, 9:26am
I doubt she was banned in so short a time period; she deleted her posts within 5 minutes of her outburst, unless some moderator just happened to be there at the time...
Title: Re: Bummer Train Ride
Post by SMQ on Oct 12th, 2007, 9:30am
Yeah, you have to work a heck of a lot harder than that to get banned around here. ;)

--SMQ
Title: Re: Bummer Train Ride (JP05)
Post by Ghost Sniper on Oct 12th, 2007, 10:17am
Man, looks like we'll have to be more careful what we say around here, or else JP05's little episode might repeat again, and maybe this time it might be coming from a more prestigious member, like Barukh or Grimby, to name a few.
Title: Re: Bummer Train Ride (JP05)
Post by Michael_Dagg on Oct 12th, 2007, 3:23pm
I believe one of the objectives for this problem is to
discover commutation of conditional probabilities and
one of the questions (which I won;t say) gives you a
hint as to how to show it. This says that your chances
of survival has nothing to do with who may pick first.
Title: Re: Bummer Train Ride (JP05)
Post by FiBsTeR on Oct 12th, 2007, 4:19pm

on 10/12/07 at 15:23:38, Michael_Dagg wrote:
This says that your chances
of survival has nothing to do with who may pick first.


When is this true, though? Suppose I have 10 chocolates, 9 of which are poisoned. Me and you take turns eating until one person is poisoned, after which the game ends. Would you really opt to go first rather than second?
Title: Re: Bummer Train Ride (JP05)
Post by Michael_Dagg on Oct 12th, 2007, 6:45pm
It is always true.

I believe you need to reread the problem
(at least as I have read it) an therefore
conclude that the "game " only ends when
we have "two" results, not just one. This really
pretty simple in fact.
Title: Re: Bummer Train Ride (JP05)
Post by kindy_kid on Oct 14th, 2007, 8:34pm

on 10/12/07 at 10:17:30, Ghost Sniper wrote:
Man, looks like we'll have to be more careful what we say around here, or else JP05's little episode might repeat again, and maybe this time it might be coming from a more prestigious member, like Barukh or Grimby, to name a few.


Maybe JP05 ate a poisoned chocolate and deleted her posts before dying. Hope Barukh and Grimbal don't eat the other poisoned chocolates. B & G: are you guys brother and sister, and are you ticketless on the train?
Title: Re: Bummer Train Ride (JP05)
Post by Grimbal on Oct 15th, 2007, 3:01am
Who exactly do you see in the role of the sister? >:(
I think I gonna cancel my account. :P

By the way, for the original problem:
"The conductor decides to punish you by offering the two of you a box of what appear to be nine identical chocolates, three of which are filled with poison."
Don't eat the chocolate, keep the evidence and sue the pervert conductor.  Get millions from the railroad company and retire.

That gives
(i) 1  (ii) 1  (iii) you won't  (iv) no.  (v) 1
Title: Re: Bummer Train Ride (JP05)
Post by kindy_kid on Oct 15th, 2007, 5:26am

on 10/15/07 at 03:01:12, Grimbal wrote:
Who exactly do you see in the role of the sister? >:(
I think I gonna cancel my account. :P


I can't see any gender icon for you Grimbal, just a recycle bin - terribly confused, no offence please!
Title: Re: Bummer Train Ride (JP05)
Post by DC1E2L on Oct 15th, 2007, 5:46am

on 10/15/07 at 05:26:04, kindy_kid wrote:
I can't see any gender icon for you Grimbal, just a recycle bin - terribly confused, no offence please!

You just have to search around to find an answer, Grimbal is male.

BTW Grimbal, you referenced in the Minimum-Cut-Length thread that SWF was male. Where does it ever say that.
Title: Re: Bummer Train Ride (JP05)
Post by FiBsTeR on Oct 15th, 2007, 6:19am

on 10/13/07 at 12:47:22, Grimbal wrote:
And I don't know yet why my result doesn't match SWF's.  That is why I wanted to reproduce his result.


Mike, the pronoun his can be considered a generic or universal pronoun (http://en.wikipedia.org/wiki/Gender-specific_pronoun#Generic_usage), in that it is not gender-specific. No matter if SWF is male or female, or whether Grimbal knows this or not, I think the usage of his is acceptable.
Title: Re: Bummer Train Ride (JP05)
Post by Grimbal on Oct 15th, 2007, 7:29am

on 10/15/07 at 05:26:04, kindy_kid wrote:
I can't see any gender icon for you Grimbal, just a recycle bin - terribly confused, no offence please!


on 10/15/07 at 05:46:37, DC1E2L wrote:
BTW Grimbal, you referenced in the Minimum-Cut-Length thread that SWF was male. Where does it ever say that.

Well, you both got a point here.  I won't cancel my account after all...  :)
Title: Re: Bummer Train Ride (JP05)
Post by Michael_Dagg on Oct 15th, 2007, 8:09am
Looking back, it seems that this person posted some interesting
problems over a period of time, which cannot be determined now.

There just doesn't seem to be enough in the transcript of this
thread that would lead anyone to get offended and delete their
membership.

So, I must speculate that the offending post(s) (if any) have been
deleted as well?
Title: Re: Bummer Train Ride (JP05)
Post by rmsgrey on Oct 15th, 2007, 12:48pm

on 10/15/07 at 06:19:05, FiBsTeR wrote:
Mike, the pronoun his can be considered a generic or universal pronoun (http://en.wikipedia.org/wiki/Gender-specific_pronoun#Generic_usage), in that it is not gender-specific. No matter if SWF is male or female, or whether Grimbal knows this or not, I think the usage of his is acceptable.

If Grimbal knows SWF to be female, then I would consider his use of "his" to be incorrect. In the other cases (Grimbal knows SWF to be male; Grimbal doesn't know SWF's gender), "his" is undoubtedly correct.

My understanding is that the masculine pronoun is traditionally accepted as correct in situations where gender is unknown or uncertain, while the feminine pronoun is traditionally reserved for situations where the entity is known to be feminine.

Political Correctness denies the usage of the masculine except where gender is known to be masculine, but has yet to provide a convenient alternative.
Title: Re: Bummer Train Ride (JP05)
Post by FiBsTeR on Oct 15th, 2007, 3:11pm

on 10/15/07 at 12:48:38, rmsgrey wrote:
Political Correctness denies the usage of the masculine except where gender is known to be masculine, but has yet to provide a convenient alternative.


"They (http://en.wikipedia.org/wiki/They)" is sometimes used, although not commonly.
Title: Re: Bummer Train Ride (JP05)
Post by rmsgrey on Oct 16th, 2007, 7:12am

on 10/15/07 at 15:11:58, FiBsTeR wrote:
"They (http://en.wikipedia.org/wiki/They)" is sometimes used, although not commonly.

Ah, yes, I forgot to mention that the above only applies when the entity is known to be singular. In situations with known plurality, or unknown or uncertain number, "they" is correct.

In situations where the entity is known singular, use of "they" often feels awkward: "An unknown person stepped onto the third rail today and electrocuted [themself|themselves|himself]"
Title: Re: Bummer Train Ride (JP05)
Post by towr on Oct 16th, 2007, 10:14am

on 10/16/07 at 07:12:52, rmsgrey wrote:
In situations where the entity is known singular, use of "they" often feels awkward: "An unknown person stepped onto the third rail today and electrocuted [themself|themselves|himself]"
You can always try to work around it by restructuring the sentence
"An unknown person stepped onto the third rail today and was electrocuted"
Title: Re: Bummer Train Ride (JP05)
Post by SWF on Oct 16th, 2007, 8:25pm
Not knowing the gender of the subject, what is the correct pronoun to complete this sentence (his, her, "his or her", "her or his", their, or its)?

"The nurse accidently spilled blood on ______ white dress."
Title: Re: Bummer Train Ride (JP05)
Post by DC1E2L on Oct 17th, 2007, 12:17am

on 10/16/07 at 20:25:01, SWF wrote:
Not knowing the gender of the subject, what is the correct pronoun to complete this sentence (his, her, "his or her", "her or his", their, or its)?

"The nurse accidently spilled blood on ______ white dress."

I would say their. :-/
Title: Re: Bummer Train Ride (JP05)
Post by Grimbal on Oct 17th, 2007, 12:49am
I would say "a".  :)
Title: Re: Bummer Train Ride (JP05)
Post by rmsgrey on Oct 17th, 2007, 4:47am

on 10/16/07 at 20:25:01, SWF wrote:
Not knowing the gender of the subject, what is the correct pronoun to complete this sentence (his, her, "his or her", "her or his", their, or its)?

"The nurse accidently spilled blood on ______ white dress."

I would say that the sentence is unlikely to arise naturally in a situation where the speaker doesn't know the nurse's gender. Were it just a reference to a nurse, without the additional gender cue of the dress, I'd incline toward "his". As it is, there's a strong expectation of femininity (the nurse possesses women's clothing) so I'd invert the normal usage:
"The nurse accidentally spilled blood on her white dress."


Of course, with more context, I might decide to revert to the more generically correct "his"


Where there's information to suggest a particular gender strongly, using the other gender for pronouns suggests you have sufficient additional information to make that correction.
Title: Re: Bummer Train Ride (JP05)
Post by Ghost Sniper on Oct 17th, 2007, 11:10am

on 10/16/07 at 20:25:01, SWF wrote:
Not knowing the gender of the subject, what is the correct pronoun to complete this sentence (his, her, "his or her", "her or his", their, or its)?

"The nurse accidently spilled blood on ______ white dress."



on 10/17/07 at 00:17:43, DC1E2L wrote:
I would say their. :-/



on 10/16/07 at 07:12:52, rmsgrey wrote:
Ah, yes, I forgot to mention that the above only applies when the entity is known to be singular. In situations with known plurality, or unknown or uncertain number, "they" is correct.

In situations where the entity is known singular, use of "they" often feels awkward: "An unknown person stepped onto the third rail today and electrocuted [themself|themselves|himself]"


My English teacher absolutely drilled this into my head. If the ANTECENDENT IS SINGULAR, THEN WHATEVER FOLLOWS HAS TO BE SINGLUAR. so saying "The nurse accidentally spilled blood on 'their' dress" drives me nuts.  :P
Title: Re: Bummer Train Ride (JP05)
Post by Grimbal on Oct 17th, 2007, 2:16pm
What about "The CIA accidentally spilled blood on their white hands"?
Title: Re: Bummer Train Ride (JP05)
Post by JiNbOtAk on Oct 17th, 2007, 9:48pm

on 10/16/07 at 20:25:01, SWF wrote:
Not knowing the gender of the subject, what is the correct pronoun to complete this sentence (his, her, "his or her", "her or his", their, or its)?

"The nurse accidently spilled blood on ______ white dress."


If "his" is correct, it would give the idea that the dress belong to the nurse ( male or female ). Wouldn't it be weird for a male ( nurse or otherwise ) to own a dress ?
Title: Re: Bummer Train Ride (JP05)
Post by towr on Oct 17th, 2007, 11:55pm

on 10/17/07 at 21:48:58, JiNbOtAk wrote:
If "his" is correct, it would give the idea that the dress belong to the nurse ( male or female ). Wouldn't it be weird for a male ( nurse or otherwise ) to own a dress ?
That depends; "dress" can be just anything you're dressed in. Most likely, if it was used for a male, it would be formal attire (although, then it's unlikely to be white, in these parts).


Quote:
dress    
–noun
1.an outer garment for women and girls, consisting of bodice and skirt in one piece.
2.clothing; apparel; garb: The dress of the 18th century was colorful.
3.formal attire.
4.a particular form of appearance; guise.
5.outer covering, as the plumage of birds.
Title: Re: Bummer Train Ride (JP05)
Post by Ghost Sniper on Oct 18th, 2007, 5:47am

on 10/17/07 at 14:16:18, Grimbal wrote:
What about "The CIA accidentally spilled blood on their white hands"?


Doesn't work. The CIA cannot be counted, so it counts as a singular antecedent. However, it cannot be referred to "he" or "she" so the correct sentence would be "The CIA accidently spilled blood on its white hands."

Most likely, the CIA wouldn't all be in one place at once, so the most logical correction of the sentence would probably be "The CIA agent spilled blood on his/her white hands."
Title: Re: Bummer Train Ride (JP05)
Post by Grimbal on Oct 18th, 2007, 5:51am
The information would probably be censored...
Title: Re: Bummer Train Ride (JP05)
Post by towr on Oct 18th, 2007, 5:58am

on 10/18/07 at 05:47:55, Ghost Sniper wrote:
Doesn't work. The CIA cannot be counted, so it counts as a singular antecedent.
Why not? It is a group made up of people, isn't it?
Afaik, you can refer to a group as singular or plural.


Quote:
However, it cannot be referred to "he" or "she"
"She" seems to be commonplace to refer to organizations/institutions. So why not here?


Quote:
so the correct sentence would be "The CIA accidently spilled blood on its white hands."
I don't see a reason to limit correctness to a single option. All three seem fine with me.
Title: Re: Bummer Train Ride (JP05)
Post by Ghost Sniper on Oct 18th, 2007, 6:16am

on 10/18/07 at 05:58:24, towr wrote:
Why not? It is a group made up of people, isn't it?
Afaik, you can refer to a group as singular or plural.


It is a group. However, if you are referring to a group collectively, then you must count it as a singular antecedent. E.g. The baseball team tried hard, but it still lost the match.
If you are referring to the group individually, then it is counted as a singular antecedent. E.g. The baseball team put on their own jerseys.
Title: Re: Bummer Train Ride (JP05)
Post by towr on Oct 18th, 2007, 7:01am
It wouldn't be a stretch to say that if a group collectively has blood on its hand, then the group individually have blood on their hands. At least in as much as they have an inkling of a clue as to what their group does.
Title: Re: Bummer Train Ride (JP05)
Post by Ghost Sniper on Oct 19th, 2007, 4:45am

on 10/18/07 at 07:01:15, towr wrote:
It wouldn't be a stretch to say that if a group collectively has blood on its hand, then the group individually have blood on their hands. At least in as much as they have an inkling of a clue as to what their group does.


That's possible, I guess, but the way Grimby worded it made it sound like he is talking about the CIA as a collective group, and that's why I said "it".

However, "he/she/it" are not interchangeable with "they", so both of them cannot be correct at the same time, and only one can work at a time.


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