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simple but tricky probability question
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Date: January 19th, 2019 9:09 PM Author: Blathering Round Eye You're about to get on a plane to Seattle. You want to know if you should bring a raincoat. You call 3 random friends of yours who live there and ask each independently if it's raining. Each of your friends has a 2/3 chance of telling you the truth and a 1/3 chance of messing with you by lying. All 3 friends tell you that "Yes" it is raining. What is the probability that it's actually raining in Seattle?
A) 8/27
B) 26/27
C) 8/9
D) 1/27
Explain your reasoning along with your answer |
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Date: January 19th, 2019 9:43 PM Author: Motley aqua kitchen Not answerable with the info given, hth. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37623375) |
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Date: January 20th, 2019 12:53 AM Author: elite brindle pistol the answer he wants is 8/9, but you are correct. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624392) |
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Date: January 20th, 2019 12:59 AM Author: Motley aqua kitchen That’s not what the answer key says! Lmao
🔑 |
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Date: January 20th, 2019 1:01 AM Author: elite brindle pistol given that it's the only answer that makes sense, what's the probability that OP is reading the answer key wrong? (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624443) |
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Date: January 20th, 2019 1:02 AM Author: Motley aqua kitchen What is the probability I’m gay? (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624457) |
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Date: January 20th, 2019 1:03 AM Author: bateful misunderstood boistinker church there's no answer key this is apparently some interview question asked to data scientists
i thought it was a gmat question because op is JJC |
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Date: January 20th, 2019 1:04 AM Author: elite brindle pistol 180, so it's intentionally poorly posed so the good candidates can catch it (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624480) |
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Date: January 20th, 2019 1:09 AM Author: Motley aqua kitchen 180 (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624521) |
Date: January 19th, 2019 9:13 PM Author: Blathering Round Eye (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37623231) |
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Date: January 19th, 2019 9:14 PM Author: Motley aqua kitchen It’s 1 or 0. Either it is raining or it isn’t. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37623237) |
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Date: January 19th, 2019 9:16 PM Author: Blathering Round Eye (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37623249) |
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Date: January 19th, 2019 9:19 PM Author: Appetizing peach chapel 26/27? Chance of one guy messing with you = 1/3. Chance of all 3 messing with you = 1/3*1/3*1/3= 1/27. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37623262) |
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Date: January 19th, 2019 9:22 PM Author: twisted brunch (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37623275) |
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Date: January 19th, 2019 9:43 PM Author: Blathering Round Eye (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37623377) |
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Date: January 19th, 2019 9:46 PM Author: Motley aqua kitchen Don’t blank please. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37623388) |
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Date: January 20th, 2019 12:45 AM Author: Motley aqua kitchen You computed the probability they are all lying (absent any other info). This is not the probability you want. Please try again. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624338) |
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Date: January 19th, 2019 9:21 PM Author: Underhanded Pungent Queen Of The Night 26/27
Easier to do it backwards and say what are the odds that all three are lying.
1/3 * 1/3 * 1/3 = 1/27
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Date: January 19th, 2019 9:24 PM Author: Odious Cerise Corn Cake Gaming Laptop It's D...1 out of the 3 is lying. If they all say yes, chances are very very good it won't rain (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37623289) |
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Date: January 19th, 2019 9:47 PM Author: Motley aqua kitchen Impoasible to answer without choosing a prior for the probability it’s raining. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37623392) |
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Date: January 20th, 2019 12:17 AM Author: Blathering Round Eye why? (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624155) |
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Date: January 20th, 2019 12:36 AM Author: Motley aqua kitchen There’s a formula for this. It’s called Bayes rule. Wikipedia it.
You need a prior distribution to compute it. Think about the intended solution and you’ll see there’s an implicit (and implausible) prior distribution assumed. |
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Date: January 20th, 2019 1:01 AM Author: elite brindle pistol (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624447) |
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Date: January 20th, 2019 1:08 AM Author: Dead university I don’t think you a priori info for this. You only need one motherfucker to be telling the truth for it to be raining. So then it’s 1-P(everyone lying) (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624518) |
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Date: January 20th, 2019 1:10 AM Author: Motley aqua kitchen You’re just considering the possibility that it’s raining and no one is lying. You also need to consider the possibility it isn’t raining and EVERYONE is lying. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624532) |
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Date: January 20th, 2019 1:13 AM Author: Dead university Fuck (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624548) |
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Date: January 20th, 2019 1:25 AM Author: Dead university I may be going full retard here, but if it isn’t raining then there is a 1/27 chance they all lie and say yes. Which still implies a 26/27 chance that it’s actually raining no? (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624622) |
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Date: January 20th, 2019 1:32 AM Author: Motley aqua kitchen Now consider the other case. Got them mixed up above. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624649) |
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Date: January 20th, 2019 1:13 AM Author: elite brindle pistol if it never rains in seattle, the probability that they're all lying is 100%. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624551) |
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Date: January 20th, 2019 4:05 PM Author: Motley aqua kitchen (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37627453) |
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Date: January 19th, 2019 9:50 PM Author: Laughsome Ape Karate Haven't thought about it too long, but I think it's 8/9
Edit: There's 27 ways (combinations) they could answer the question.
They all said "yes". This can only happen if they're all telling the truth, or all lying.
There's 8/27 ways they could all be telling the truth (2/3 to the power of 3).
There's 1/27 ways they could all be lying (1/3 to the power of 3).
So of the 9 ways they could have all answered "yes", 8 have them telling the truth and 1 has them lying, therefore 8/9 chance of telling the truth. |
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Date: January 20th, 2019 12:17 AM Author: Blathering Round Eye i also thought 8/9 but the answer key says 26/27
I think the answer really depends on the phrasing of the question. and given that all 3 said "YES its raining" the probability that it is indeed raining is 1-probability they all lied. so it is 26/27
after thinking a little bit more i think 8/9 would be the answer if the question was phrased as "given that all 3 replied the same way what is the probability that it is raining". but the question asked here is different and explicitly says that all said YES |
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Date: January 20th, 2019 12:34 AM Author: Motley aqua kitchen I believe this is the intended but wrong answer. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624283) |
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Date: January 20th, 2019 12:22 AM Author: crystalline comical garrison (xo 2019) (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624180) |
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Date: January 20th, 2019 12:25 AM Author: bateful misunderstood boistinker church getting another MBA jjc? (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624214) |
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Date: January 20th, 2019 12:52 AM Author: elite brindle pistol 100% (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624385) |
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Date: January 20th, 2019 1:32 AM Author: passionate skinny woman Haven’t read the thread yet.
You know that they’re either all lying (it’s not raining) or all telling the truth (it is raining).
Odds that they’re all lying are 1/27 (1/3^3).
Odds that they’re all telling the truth are 8/27 (2/3^3).
The other 18/27 possible states don’t matter.
So, 8 times out of 9, it’s raining. |
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Date: January 20th, 2019 1:34 AM Author: Motley aqua kitchen Maybe you should read the thread. We’ve been over this. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624663) |
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Date: January 20th, 2019 1:35 AM Author: passionate skinny woman I wanted to read it first.
Fuck, now I see it depends on the base rate.
I haven’t thought about bayes rule in like 10 years. |
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Date: January 20th, 2019 4:31 AM Author: Lilac internet-worthy hall 8p/(7p+1) (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37624942) |
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Date: January 20th, 2019 8:01 AM Author: alcoholic milky center telephone assuming that p is the prior probability of rain it's this one (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37625178) |
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Date: January 20th, 2019 2:49 PM Author: Motley aqua kitchen (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37626892) |
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Date: January 20th, 2019 2:53 PM Author: alcoholic milky center telephone bro the right answer has already been posted (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37626916) |
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Date: January 20th, 2019 2:55 PM Author: Motley aqua kitchen 🍆 (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37626922) |
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Date: January 20th, 2019 2:59 PM Author: magical private investor travel guidebook Jfc lawboys
The only way it is NOT RAINIING is the 1/27 chance ALL OF THEM are fucking with you
Its like saying there you have three radars across Seattle. The radars are accurate 2 out of three times. You check the radars and they all indicate that it's raining. What is the probability it is raining in Seattle (in one part, the whole city, it doesn't matter)?
For it to be NOT RAINING all three radars have to be wrong.
Math major and this took me less than two seconds to think through op |
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Date: January 20th, 2019 3:04 PM Author: Motley aqua kitchen Your school should rescind your math degree. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37626968) |
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Date: January 20th, 2019 3:07 PM Author: magical private investor travel guidebook Brother it doesn't matter if one of your boys is fucking with you. Two of them can be fucking with you and as long as your last bro is telling the truth, IT'S FUCKING RAINING (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37626982) |
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Date: January 20th, 2019 3:08 PM Author: Motley aqua kitchen Did you even read the thread? We’ve been over this. You’re wrong. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37626988) |
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Date: January 20th, 2019 3:14 PM Author: magical private investor travel guidebook I did read the thread and you are splerging out. OP wanted an explanation of why answer key said D. You came in here mucking up the thread, confusing ppl, and citing uncessary shit. Classic law boy trying to outsmart the hypo
Can you even explain your reasoning?
I can't even believe this thread made it this far. This is literally some high school level shit
Edit: Im pretty sure the part that trips you and other law Boys up is that only one friend needs to be telling the truth, therefore, all of them have to be lying for it to be not raining |
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Date: January 20th, 2019 3:46 PM Author: Motley aqua kitchen Do you understand Bayes rule?
There are two possibilities: it’s raining and they’re all telling the truth, or it’s not raining and they’re all lying. You must account for both.
Jfc and don’t you purportedly work in finance? |
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Date: January 20th, 2019 4:09 PM Author: magical private investor travel guidebook Trader and I don't consider my job "finance"
As OP said, this is a very simple probability question. You've shitted up the whole thread citing irrelevant shit and have somehow convinced yourself that the answer key is wrong along the way lol
What you said makes no sense |
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Date: January 20th, 2019 4:12 PM Author: Motley aqua kitchen Answer the question. Do you understand Bayes rule? (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37627536) |
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Date: January 20th, 2019 4:14 PM Author: magical private investor travel guidebook You are frustrated and gakked out and I am leaving this subthread (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37627552) |
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Date: January 20th, 2019 4:16 PM Author: Motley aqua kitchen See below. You’re not computing the right probability. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37627577) |
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Date: January 20th, 2019 4:11 PM Author: magical private investor travel guidebook Explain to me how it can not be raining unless all are lying to you (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37627522) |
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Date: January 20th, 2019 4:16 PM Author: Motley aqua kitchen You’re confusing the desired conditional probability with the probability of them lying a priori, I think.
Do you agree the answer we seek is the probability of it raining conditional on all three friends saying it’s raining? |
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Date: January 20th, 2019 4:20 PM Author: magical private investor travel guidebook omg dude this is not a conditional probably Q
I've given you the benefit of the doubt and treated you with wayyyyy too much respect thus far. Lmao I am officially OUT of this thread now. Waste of time |
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Date: January 20th, 2019 4:21 PM Author: Motley aqua kitchen Yes it is. Are you high?
You are computing some probability conditional on some given information (three friends say it’s raining). |
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Date: January 20th, 2019 4:32 PM Author: magical private investor travel guidebook Great response on stack exchange about this Q:
"Each of the above analyses fail to assess the logic of the question primarily in their approach. Since all three say it is raining, you cannot approach the solution by determining each friend's propensity for truth. For it not to be raining, they ALL must be lying. Therefore, the solution must be the inverse of the probability that all three are "messing with you." (1/3)x(1/3)x(1/3)=1/27 (3.7% chance they are all lying). Since there is only a 3.7% chance all three friends are messing with you, there is a 96.3% chance it is raining."
This is a great interview question because someone like me will be able to quickly determine the goal of the question, map my way to an answer and walk the interviewer through my process, and then explain my answer to contemplate any potential problems or shortcomings of my answer. Meanwhile, someone like you will be splerging out and flailing their arms about some irrelevant shit, scribbling down numbers and gook hyroglypbics on your paper, before telling the interviewer the Q can be answered after 15 minutes. Then you go home an admire your genius for "winning" the trick question |
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Date: January 20th, 2019 4:40 PM Author: Motley aqua kitchen Not responsive to my inquiry. Congratulations on finding someone else on the internet who is also wrong, I guess.
The issue you’re missing is that the probability of them lying a priori is not the probability of their utterances being false after you’ve been given the information all three say it’s raining. Think about a situation where it never rains in Seattle, for example. |
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Date: January 20th, 2019 4:36 PM Author: magical private investor travel guidebook And BTW, just to complete ur gaping: I actually was asked this Q in round two for my first job. They asked that, the three marbles Q, how many times to fold a piece of paper to reach the moon, and 98*36 (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37627765) |
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Date: January 20th, 2019 4:41 PM Author: Motley aqua kitchen Ok now you’re just trolling me. Good work. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37627789) |
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Date: January 20th, 2019 7:29 PM Author: Laughsome Ape Karate 1/27 is the probability that you poll them and they a) all say it's raining and b) it turns out it's not raining.
Given they all said it's raining, the range of possible situations changes from 27 to 9, and in 8 of them Seattle is raining.
(This all assumes the probability of raining/not raining is 50/50) |
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Date: January 20th, 2019 3:07 PM Author: Motley aqua kitchen Date: January 20th, 2019 2:59 PM Author: Mormon missionary (only posts on WSHH and xo)
Jfc lawboys The only way it is NOT RAINIING is the 1/27 chance ALL OF THEM are fucking with you
Its like saying there you have three radars across Seattle. The radars are accurate 2 out of three times. You check the radars and they all indicate that it's raining. What is the probability it is raining in Seattle (in one part, the whole city, it doesn't matter)?
For it to be NOT RAINING all three radars have to be wrong.
Math major and this took me less than two seconds to think through op
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Date: January 20th, 2019 4:11 PM Author: vivacious athletic conference electric furnace my brain is too old and tired to even think about attempting this problem or giving a shit about this lmao. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37627523) |
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Date: January 20th, 2019 4:19 PM Author: Bright plaza you can look up the weather in Seattle on an app (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37627605) |
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Date: January 20th, 2019 4:24 PM Author: Poppy whorehouse toilet seat Odd that you posed a question referencing the existence of "friends," JJC. Branching out to SciFi now? (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37627648) |
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Date: January 20th, 2019 5:13 PM Author: avocado excitant halford Good discussion of the problem. Spoiler "Bayes's Theorem is not optional."
http://allendowney.blogspot.com/2016/09/bayess-theorem-is-not-optional.html?m=1 |
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Date: January 20th, 2019 5:44 PM Author: Motley aqua kitchen (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37628220) |
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Date: January 20th, 2019 7:26 PM Author: Motley aqua kitchen (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37629020) |
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Date: January 20th, 2019 5:14 PM Author: charismatic brethren headpube That's not how weather works. (http://www.autoadmit.com/thread.php?thread_id=4181520&forum_id=2#37627948) |