# Is this a valid inference? **URL:** \ **Category:** In My Humble Opinion\ **Created:** [April 11, 2012, 11:25pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507 "2012-04-11T23:25:11Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [April 12, 2012, 5:37am UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/21 "2012-04-12T05:37:38Z")
> [@Max\_the\_Immortal](#): > > Okay, fine. But doesn’t make it a _useful_ inference if you’re trying to discover vampires. I thought we were looking for organ players? Damn this stuff is confusing. ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [April 12, 2012, 5:56am UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/22 "2012-04-12T05:56:18Z")
> [@Max\_the\_Immortal](#): > > Okay, fine. But doesn’t make it a _useful_ inference if you’re trying to discover vampires. Sure it does, if you know this fact, you know you’re going to have more luck trying to find vampires by trolling those riveting organ player parties than wandering around aimlessly in a random neighborhood with no direction. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [April 12, 2012, 7:32am UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/23 "2012-04-12T07:32:58Z")
For what it’s worth: Given: P(O|V) \> P(O|-V) And from basic probability: P(O|V)P(V) + P(O|-V)P(-V) = P(O) Substitute (assume P(-V) \> 0): P(O|V)P(V) + P(O|V)P(-V) \> P(O) P(O|V)(P(V) + P(-V)) \> P(O) P(O|V) \> P(O) Use Bayes’ formula: P(V|O)P(O)/P(V) \> P(O) P(V|O)/P(V) \> 1 P(V|O) \> P(V) And there you go. ---
**Author:** ![TokyoBayer](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tokyobayer/32/13989_2.png) [@TokyoBayer](https://boards.straightdope.com/u/TokyoBayer)\ **Post date:** [April 12, 2012, 12:11pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/24 "2012-04-12T12:11:15Z")
> [@Jragon](#): > > > [@ShibbOleth](#): > > > > Let’s say there is one vampire in the world. She is an organ player. Therefore 100% of vampires are organ players. Then there are 7,000,000,000 people in the world who are not vampires. Of those, 0.01% play the organ. That means that while vampires are more likely to play the organ than a non vampire, there are 700,000 non vampire organ players in the world. If I hear someone playing the organ, I’m generally going to assume that they are not a vampire. > > Yes, but the key term is **more likely**. The chance of a given non-organ player being a vampire, in this case, is 0, while the chance of an organ player being a vampire is 1/700,000. Therefore, it is safe to assume that an organ player is more **likely** to be a vampire than a non-organ player, even if the overall probability is still absurdly low. > > In other words, it’s more likely for an organ player to be a vampire THAN A NON-ORGAN PLAYER. But it doesn’t follow from that (necessarily) that an organ player is more likely to be a vampire than ANOTHER ORGAN PLAYER. ShibbOleth’s example is incorrect, according to followup by the OP, there are non-organ playing vampires as well. So let’s assume there are ten vampires, one who plays the organ and nine who don’t. The odds that an organ player is a vampire is 0.000143% while the odds that someone in the general population is 0.0000143% Sure, an organ player is technically “more likely” to be a vampire, but it’s statistically insignificant. The chance of an organ player being human is 99.9998571% vs. 99.9999857% of the general population. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [April 12, 2012, 12:30pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/25 "2012-04-12T12:30:18Z")
Impossible to say without at least knowing the ratio of vampires to mortals. The poll needs an option 3. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [April 12, 2012, 2:00pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/26 "2012-04-12T14:00:00Z")
> [@Mangetout](#): > > Impossible to say without at least knowing the ratio of vampires to mortals. The poll needs an option 3. I think that you’re trying to figure out whether an organ player is more likely to be a vampire than not, which is a different question from what I’m asking. I should’ve made that explicit in the OP. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [April 12, 2012, 2:12pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/27 "2012-04-12T14:12:00Z")
> [@Mangetout](#): > > Impossible to say without at least knowing the ratio of vampires to mortals. The poll needs an option 3. > [@ultrafilter](#): > > I think that you’re trying to figure out whether an organ player is more likely to be a vampire than not, which is a different question from what I’m asking. I should’ve made that explicit in the OP. We know there’s a greater ratio of vampire organ players than mortal organ players. The phrasing of the question is a little off, but on the re-read I picked up the intent. It’s really not a lack of information that’s the problem, it’s the lack of specificity in the question. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [April 12, 2012, 2:40pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/28 "2012-04-12T14:40:09Z")
> [@TriPolar](#): > > We know there’s a greater ratio of vampire organ players than mortal organ players. The phrasing of the question is a little off, but on the re-read I picked up the intent. It’s really not a lack of information that’s the problem, it’s the lack of specificity in the question. How would you phrase it? ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [April 12, 2012, 2:43pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/29 "2012-04-12T14:43:58Z")
> [@ultrafilter](#): > > How would you phrase it? Probably in C or Java. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [April 12, 2012, 2:46pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/30 "2012-04-12T14:46:01Z")
> [@TriPolar](#): > > Probably in C or Java. So you don’t know? ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [April 12, 2012, 2:51pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/31 "2012-04-12T14:51:15Z")
> [@ultrafilter](#): > > I think that you’re trying to figure out whether an organ player is more likely to be a vampire than not, which is a different question from what I’m asking. I should’ve made that explicit in the OP. I misread the question as asking this, but that’s entirely my fault. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [April 12, 2012, 2:52pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/32 "2012-04-12T14:52:29Z")
> [@ultrafilter](#): > > So you don’t know? I’m not good at that. The syntax and semantics of spoken languages start a fight in my head. So I prefer to reduce such things to a technical language. To me the question sounds like you’re restating the premise. If there is a higher percentage of vampire organ players than non-vampire organ players is there a higher percentage of vampire organ players than non-vampire organ players? ---
**Author:** ![Nava](https://avatars.discourse-cdn.com/v4/letter/n/da6949/32.png) [@Nava](https://boards.straightdope.com/u/Nava)\ **Post date:** [April 12, 2012, 3:01pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/33 "2012-04-12T15:01:45Z")
I think many people are being confused by the question of “how likely would an organ-player be to be a vampire”, which is a completely different one. The question of whether “if Elbonia has a greater F:M ratio than the rest of the world, does that mean that an Elbonian has a greater probability of being female than people from the rest of the world do?” does not depend on whether the ratio is 100000:1, 2:1 or 1001:1000. The question of whether the difference is important, relevant, something to worry about, or what is the actual probability of an Elbonian being female… do depend on that ratio. ---
**Author:** ![Chessic\_Sense](https://avatars.discourse-cdn.com/v4/letter/c/7c8e57/32.png) [@Chessic\_Sense](https://boards.straightdope.com/u/Chessic_Sense)\ **Post date:** [April 12, 2012, 3:03pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/34 "2012-04-12T15:03:51Z")
> [@ultrafilter](#): > > If you learn that someone is an organ player, does that make them more likely to be a vampire than someone who doesn’t? So you want to know if P(V|O) \> P(V|-O)? Then yes, this was proven by **Lubricious**. ---
**Author:** ![Heart\_of\_Dorkness](https://avatars.discourse-cdn.com/v4/letter/h/4bbf92/32.png) [@Heart\_of\_Dorkness](https://boards.straightdope.com/u/Heart_of_Dorkness)\ **Post date:** [April 12, 2012, 3:06pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/35 "2012-04-12T15:06:58Z")
> [@ultrafilter](#): > > I think that you’re trying to figure out whether an organ player is more likely to be a vampire than not, which is a different question from what I’m asking. I should’ve made that explicit in the OP. > [@ultrafilter](#): > > How would you phrase it? I read it the wrong way at first, and this may be part of the reason why: I read the first part of the question, “If you learn that someone is an organ player, does that make them more likely to be a vampire…”, took that as the intended question, and unconsciously assumed the antecedent was something like “…than not”. I apparently either ignored the implication of “doesn’t”, or transformed it in my mind to “isn’t”. If you had said “…than someone who doesn’t _play the organ_,” then I might have gotten it right the first time. Even better, though, would be to say something like, “If you learn that someone is an organ player, are they more likely than a non-organ-player to be a vampire?” or “Who is more likely to be a vampire? An organ player, or a non-organ-player (or neither)?” And part of the problem may be that it’s relatively common to see _invalid_ inferences along the lines of, “Vampires are more likely than non-vampires to play the organ; therefore, an organ player is more likely to be a vampire than a non-vampire,” and so some people may be primed to look for this this type of error. ---
**Author:** ![Boyo\_Jim](https://avatars.discourse-cdn.com/v4/letter/b/87869e/32.png) [@Boyo\_Jim](https://boards.straightdope.com/u/Boyo_Jim)\ **Post date:** [April 12, 2012, 3:27pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/36 "2012-04-12T15:27:07Z")
Ok, now you’re really confusing me, because of this post: > [@ultrafilter](#): > > I think that you’re trying to figure out whether an organ player is more likely to be a vampire than **not** , which is a different question from what I’m asking. I should’ve made that explicit in the OP. Your poll question is > [@](#): > > Is the organ player more likely to be a vampire? At only difference between the two, AFAIK, is the “not” that I bolded in your post. So… back to your poll question… Is the organ player more likely to be a vampire **[than WHAT]**? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [April 12, 2012, 3:32pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/37 "2012-04-12T15:32:57Z")
> [@Boyo\_Jim](#): > > So… back to your poll question… Is the organ player more likely to be a vampire **[than WHAT]**? The question is in the OP. Do people really answer polls without reading anything else? ---
**Author:** ![MichaelEmouse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/michaelemouse/32/101_2.png) [@MichaelEmouse](https://boards.straightdope.com/u/MichaelEmouse)\ **Post date:** [April 12, 2012, 3:37pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/38 "2012-04-12T15:37:04Z")
Boyo, There are two possibilities I see: 1. Is the organ player more likely to be a vampire than not a vampire? 2. Is the organ player more likely to be a vampire than a non-organ player is likely to be a vampire? I think Ultra means 2, not 1. If we take question 1, we do not have enough information to come to a conclusion. If we take question 2, we do have enough information. Whether that increase in likelihood is significant or insignificant is a distinct question. ---
**Author:** ![Heart\_of\_Dorkness](https://avatars.discourse-cdn.com/v4/letter/h/4bbf92/32.png) [@Heart\_of\_Dorkness](https://boards.straightdope.com/u/Heart_of_Dorkness)\ **Post date:** [April 12, 2012, 3:47pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/39 "2012-04-12T15:47:42Z")
> [@ultrafilter](#): > > The question is in the OP. Yes, but even in the OP, it’s phrased in a way that is easy to misread, as I explained above. It’s not ambiguous or unclear if read correctly, but the first part of the sentence leads the reader down the garden path, because “If you learn that someone is an organ player, does that make them more likely to be a vampire?” is a complete thought in and of itself. So if you read that part and process it as the full question, you’re less likely to spot the contradiction in “doesn’t”. ---
**Author:** ![Ferret\_Herder](https://avatars.discourse-cdn.com/v4/letter/f/e47774/32.png) [@Ferret\_Herder](https://boards.straightdope.com/u/Ferret_Herder)\ **Post date:** [April 12, 2012, 4:07pm UTC](https://boards.straightdope.com/t/is-this-a-valid-inference/618507/40 "2012-04-12T16:07:58Z")
Minor nitpick: The sentence construction isn’t really grammatically proper. It should be something like, “If you learn that someone plays the organ, does that make them more likely to be a vampire than someone who doesn’t?” [Previous page](https://boards.straightdope.com/t/is-this-a-valid-inference/618507.md?page=1) [Next page](https://boards.straightdope.com/t/is-this-a-valid-inference/618507.md?page=3)