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# Question about the use of probability in proofs

• Probability theory - Wikipedia
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The "three door puzzle" is an interesting and unusual probability question. Here's how it works. You are a contestant in a game show, and the game show host tells you there is a prize behind one of the three doors you face. You have to guess which door to open. So the probability for 30 people is about 70%. And the probability for 23 people is about 50%. And the probability for 57 people is 99% (almost certain!) Simulation. We can also simulate this using random numbers. Try it yourself here, use 30 and 365 and press Go. A thousand random trials will be run and the results given. The "Probability of Precipitation" (PoP) simply describes the probability that the forecast grid/point in question will receive at least 0.01" of rain. So, in this example, there is a 40 percent probability for at least 0.01" of rain at the specific forecast point of interest! I recommend going through the Bayes updating section of this article for the understanding of the above question. 30) What is the probability of having HIV, given he tested positive on Elisa the second time as well. The prior probability of anyone having HIV is 0.00148. The true positive rate for Elisa is 93% and the true negative rate is 99%. is a statistical question because one anticipates variability in students' ages. CCSS.Math.Content.6.SP.A.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Tutorial on finding the probability of an event. In what follows, S is the sample space of the experiment in question and E is the event of interest. n(S) is the number of elements in the sample space S and n(E) is the number of elements in the event E. . Questions and their Solutions Question 1 A die is rolled, find the probability that an even number is obtained. Probability theory is the branch of mathematics concerned with probability.Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms.Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed ... A probability of 1.5 could be interpreted as you're 150% sure the event will happen - kind of like giving a 150% effort. And if you can have a probability > 1, I suppose you can have a probability < 0. Negative probabilities can be interpreted as follows. A probability of 0.001 means there's almost no chance of the event happening. A Short History of Probability From Calculus, Volume II by Tom M. Apostol (2 nd edition, John Wiley & Sons, 1969 ): "A gambler's dispute in 1654 led to the creation of a mathematical theory of probability by two famous French mathematicians, Blaise Pascal and Pierre de Fermat. Probability MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Probability with easy and logical explanations. Probability MCQ is important for exams like Banking exams,IBPS,SCC,CAT,XAT,MAT etc.

2022.01.22 03:26 gistya Question about the use of probability in proofs

To my mind, "the probability of outcome A in trial-set T is 50.000...%" is a meaningful and valid statement if and only if, given an infinite number T_n of trials in set T, exactly 50.000...% of the outcomes would be A. It follows then that, given the count A_n of outcomes A in T, and the count X_n of some other, unknown outcomes in T:

• A_n / X_n ≥ 1
• A_n + X_n ≤ T_n
• T_n / A_n = 2
• T_n / X_n ≥ 2
• A_n - X_n ≥ 0
• (A_n - X_n) % 2 = 0 or 1
• T_n must be countably infinite and even (otherwise we couldn't know the ratio between A_n and the other trials and it couldn't be exactly 50.000...%)
• A_n and X_n are both also infinite
• A_n must be odd sice T_n / 2 = A_n
Ok, so lets say I can prove that some conjecture W can only be true when T_n / 2 = A_n.
But then lets say I can also prove that A_n must be even.
Would that constitute a disproof of W?

2022.01.22 03:26 Difficas How to use this FU item? it seems that there is no wiki for the apex microscope for some reason

2022.01.22 03:26 KingKhanRaheel Students of Reddit, what's the story when your teacher was teaching something you already knew a lot about and you destroyed your teacher by proving yourself right?

2022.01.22 03:26 Esperaux “An Organisation of Militants” The Federación Anarquista Uruguaya - Tommy Lawson

2022.01.22 03:26 TuKisiRailSi Remembrance of the days when Quora used to be a good website.

Long ago, Quora used to be a good website. This is the story of how it got ruined.
As a schoolboy, I used to frequent the school quizzing circuits of Delhi. I was interested enough to use internet to become better at quizzing. In those days, Quora used to be a digital hub for quizzers. We would post fascinating questions that we ourselves had created or been asked in quizzes. Then, Hindutva/ Brahminism entered the scene.
Quora began to be flooded with answers supportive of Hindutva. My parents gave me a liberal upbringing as they are educated and we belong to a Dalit community (if you find an educated Dalit who supports BJP, then it is a person who is being a stooge for monetary gains). Although I would read these answers (I was only 12!), I would find them overblown and silly. Then one day, I read a long, cinematic story about how a user (anonymous) had been beaten by a Muslim boy who exploited the fact that he had been underweight. He did not know the boy personally, and met him four years later when he bumped into him by accident one day. By this time, he had become a muscular macho (the user must have been jerking off while typing this fantasy story). The Muslim boy tried to run the moment he saw him (it is normal to remember a person who one met only once four years ago, even though he has gained muscles since then). The user claimed to have beat the shit out of him.
I am not saying that no Muslim boy has ever beat up a Hindu boy. But the user insisted that it was because of difference of religion. In that long answer, he reminded the reader this again and again and again. I was only 12, but told myself but this was crazy. I deleted Quora a couple of days later. My quizzer friends also did the same sooner or later.
A few years later, the Dalit community had a proud moment when Tina Dabi topped the UPSC examination. I googled her name because my relatives were very pleased about the topper's identity. I found a Quora question in which a user had asked if an SC person had truly topped the exam. I read the answers. All of them said that her marks must have been increased because she belonged to a Scheduled Caste (like this happens on an annual basis).
Needless to say, I have never used Quora since then.

2022.01.22 03:26 didok 16 days today! Today is new one.

Sober for 16 days, it is not much but it is something. I can say that i am proud of myself. Spend whole afteroon and evening with my boys playing cards. They went through a case of beer while i had some tea and schweppes. I had such of good time like everybody else. Stay sober, IWNDWYT!
P.S. One of guys got shitfaced, stupid and agressive...

2022.01.22 03:26 Demy1234 Brand accounts target harassment at a single man dating women in NYC

2022.01.22 03:26 HarekuinZ No se si ya lo has visto mi kin pero esta bueno

2022.01.22 03:26 Princessbitch4 What would you like in a Fallout game?

I would love a small build your own camp, for travel when you don't wanna fast travel some distance to or from destination.wouldnt be cool to have mutated fish or rad horses?

2022.01.22 03:26 LightBlindsAtFirst Ranked Team Slayer?

So does 343 understand that most of if not all of the competitive Halo player base, wants Ranked Team Slayer? I mean Team Slayer is what made the game what it is today.
People talk about the "social aspects" of Halo 2 and 3 but that's because those people had not played online multiplayer games before or at least had not really put time into one. Experiencing social elements and making friends and enemies and all that shit, happened in a lot of online games waaaaaay before Halo. Halo didn't revolutionize shit on that aspect. But... Halo: Combat Evolved did more for console gaming than any game for the time possibly for all time. There was no other game that had brought people together physically like that game. Not just socially but IN IRL. Sure there was LAN matches in Doom and Quake and whatnot but at the time, anyone who owned an Xbox it was a challenge to be the best at Halo. There were plenty of online games that did everything "socially" that people on here love to talk about things like "community" and new friends and blah blah blah. That wasn't new to Halo. They were simply new to online gaming.
It was the competitive nature of Halo that set it apart. Yes there were more competitive games that were online but Halo CE overtook all. You could go over to a friend's house, see an Xbox on floor and challenge them to see who the best was.
It was so much more than just the online social aspect. That's what rocketed it forward into Xbox live with Halo 2 and 3. without the competition there would be no social aspect. No one cared about custom gametypes and force or w/e you plebs like. It was about who could get to 25 kills first. Who could consistently land the TSK. (People seem to forget that with the pistol in the ORIGINAL HALO not the MCC that all 3 shots must land on the head) But sadly this nature is somehow missing in Halo: Infinite. The game is what it is, Spartans are bred for war. (Although rated T LOL) Let us slay each other in glorious combat. Not objective based, or COD inspired gametypes. While those gametypes have a place, it is the deathmatch that made Halo multiplayer what it is, yes an older gametype but something that Halo built upon and expanded. It is pure and must be implemented. I would argue there is something that ignites a spark in a noob player when they get rekt on team slayer, it gives them a drive to reach that next level. In CTF or oddball or w/e this becomes muddy, slayer is Halo at it's purest.
I also ask why is everything 343 adds to Halo just straight trash. I mean what they make is already the formula that was made way before them. We wanted classic Halo gameplay, something that was ready implemented in earlier games by BUNGIE, so everything that tis not that, is added by 343 and it just is not good. Strongholds, a season pass?? What else is there that they have added to Halo? I dunno yea this is a rant but how can something like a ranked Team Slayer not be in a Halo game? It ain't Halo.

2022.01.22 03:26 AntiqueRoseEdwards Beats Fit Pro True Wireless Earbuds by Dr. Dre (Black): \$153 (Retail: \$199.99) + Free S/H

2022.01.22 03:26 Throwaway3576579 I’m 19 years old and I’m always horny and dwell onto these thoughts and I don’t know what to do.

So i’m 19M wish I was 19F tho and I’m about to be 20M in a couple months. I never had experience with any girl and nor have I ever had sex before or done anything sexual with anybody. I haven’t talked to a girl since I was 17 back in High School.
However I have had a big issue with myself. I’m always horny, whenever I’m horny I feel a big tingling sensation down my area, and I always wank off to porn or pictures of girls(NSFW content). I haven’t had this problem a year ago when I was 18 but as soon as I turned 19 I started having a problem of always wanting to jerk off and I always get hard imagining cute girls even tho I never been in a relationship before.
I also fantasize about weird stuff like being a girl/femboy daily. I dont like being horny because every time I finish jerking off I just get ‘’depressed’’ and start sleeping. I always get very curious and tend to overthink not to mention get very jealous that they’re young adults my age out there having sex and having a good time, what should I do? How do I stop being horny? I need some advice please.

2022.01.22 03:26 Revolutionary_Oil_74 Does anyone else face a problem where their fingers get sweaty while typing at high speeds?

I've had this problem for the last few months. So, basically what happens is that when I type as fast as I can, my fingers start getting sweaty. Not sure if sweaty is the right word, they just start slipping on the keys.
I tried different keyboards, cleaning the keycaps, washing hands before I type, and using finger cots (those were just uncomfortable). Nothing helped. I think it's more of a mental thing but I can't figure out how to fix it. Any help would be appreciated.

Also, this isn't for a specific speed, it's for my top speed. It used to happen when my top speed was 120, 130, and now 140

2022.01.22 03:26 sankv24 Lord ganpati!

2022.01.22 03:26 iamomkar10 Thanks to your wonderful response to my dog portrait, here's a charcoal portrait of a cat. Didnt wanted to hurt the cat community after i drew the dog so here it goes...

2022.01.22 03:26 alyy__g Insomnia

So the last week has been a big rough.
I had a sober day on monday after going hard all weekend, but tuesday and wednesday shit hit the fence again. First night I couldn't sleep at all since we took some hard drugs and even though I already felt dead on Wednesday I kept pushing it and just got so drunk that I was able to ignore it. Passed out cold for only 6 fucking hours that night.
On Thursday had like 4 beers throughout the day to keep the fear at bay and couldn't sleep. Chugged another one at 5AM and passed out for a few hours.
Yesterday I wanted to drink 2 beers in the evening but smoked so much weed that I thought one would be enough.
Here is the funny thing. I pass out every time my bf and me are watching a movie and i literally couldn't stay awake if my life depended on it, but as soon as he turns of the TV and goes to sleep himself I'm awake. Literally awake and feeling wired as he'll, unable to make myself fall asleep for hours?
What the fuck is this shit about? Is it a mental thing since I hate being alone or caused by the fact that my brain is not stimulated enough once the movie is off?
Anyways, I don't know what to do anymore, I'm so tired. So, sooo tired. Did I taper too fast off this bender even though I did have sober days in between? I don't really feel any other WD symptoms besides this fucking insomnia and a little anxiety when bf isn't around.
Option a) get back to 3 beers in the evening and hope thats enough to make me sleep a little, taper from there
Option b) i still have valium, maybe rather take 10mg before bed for a night and 5 for the next 2
Option c) maybe try some OTC medication like melatonin or some shit? Already taking CBD throughout the day but welll...
Sorry for the long post, had insomnia before but this shit is literally driving me crazy and I'd be glad about some answers or recommendations.. chairs :(

2022.01.22 03:26 Mental-Committee-344 میدونم واسه هزاران سال پیشه ولی میخوام ببینم کیا یادشونه؟ لجندا فقط میدونن

2022.01.22 03:26 jameside Server starts 4x faster after replacing ts-node with SWC

I spent a day evaluating alternatives for tsc for an API server with about 500 modules (excluding dependencies) and landed on SWC.
In development, the server used to use ts-node-dev and tsconfig-paths to compile TypeScript, rewrite path aliases (to import `~/cache/redis` from anywhere), and watch for file changes. Now nodemon with `@swc/register` does all those things. Compiling all the TypeScript now takes just 600ms and the server starts 4x faster.
SWC does a few things well. It doesn’t rely on a daemon or caches for speed. It’s just always fast.
SWC’s support for rewriting path aliases was also important. I evaluated Sucrase, which runs faster than SWC despite being written in JS in contrast with Rust. However, Sucrase doesn’t rewrite path aliases and using SWC is faster than running another program like tsconfig-paths or jscodeshift.
The biggest risk I see is for SWC to fall behind TypeScript or behave differently than tsc in subtle ways. But since SWC just needs to parse TypeScript, that’s a much easier task than implementing tsc’s type checking (for now…). And by using SWC also for production builds, there is thankfully parity between development and production.
It’s been only a day so there might be issues I haven’t found yet. There certainly are some gotchas with .swcrc and the CLI. Once everything it set up it seems to work well, though.

2022.01.22 03:26 Rare-Mistake3495 [Help] [ps4/5] [ds3] Champion gravetender

I may have screwed myself by killing freide already but if anyone is willing to help please drop a sign on the ledge before you drop into his arena. Password 351

2022.01.22 03:26 lonely-_-loser Thought this belonged here

2022.01.22 03:26 urmom_42_069 B2 cultist

I left my fiancée at the altar, after she casually brought up her idea that the B-2 was inspired by the Ho 229 a week prior. I was devastated. I locked myself inside my room for 4 days and 4 nights, watching and reading nothing but B-2 content. After my retreat I snuck into Whiteman Air Force Base and broke into a B-2 hangar. I knelt before the mighty Spirit of California, named after my home state, and prayed for it's forgiveness for an entire night. I was briefly interrupted by an Air Force Security Forces member. But they were scared away after I told them that Security Forces are a bunch of nerds who weren't cut out for actual Air Force SF. I returned to praying, I told the Spirit that my fiancée meant no harm, that she was misguided. But the machine spirit of the B-2 awoke and spoke to me. It told me of an apocalyptic future, one in which the world was consumed by a war involving two factions. Those who believed the B-2 and the Ho 229 are one and the same, lead by my fiancée. And those, lead by me, who believe the B-2 is a creation of Jack Northrop's spirit, who visited Northrop engineers in their sleep and implanted them with the knowledge they would need to create the B-2. Marrying my fiancée would've triggered a series of events that would lead to this cataclysmic war, from which the Earth would never recover from. I knew what I had to do. I covered myself in the B-2's sacred RAM coating and proceeded to walk back home. I walked without fear, as the B-2's RAM would keep me safe from all harm. No police officer would approach me. No woman would look me in the eyes. No Flanker could track me. And no fish would get in my way. I walked and walked until I reached a hill that overlooked the church where my wedding would take place. I stared down at the people in attendance, her family and mine, and our friends. They disgusted me. There they stood, praising and smiling towards a woman who dared to compare the B-2 to a failed German dorito chip. But my disgust soon disappeared... I could hear it. I looked up and there it was... a B-2 flying overhead. I was in awe of its majestic form. It opened it's holy bomb bay. And unleashed a load of it's sacred, all American, bombs onto the church. I watched in silence as the B-2 destroyed everything and everyone I knew. But I knew it was worth it, the Spirit gave me something I had always wanted... a fresh start away from those Ho 229 worshipping heretics. But only after I went to the hospital. Because apparently RAM coatings are extremely toxic. While in the hospital, I saw on TV that the B-2 I witnessed actually strayed off course from its intended training target. Why the crew thought a church in the middle of Los Angeles was a good alternative, I will never know. But I knew that the Spirit of California was watching over me. It loved me. And I love the B-2.

2022.01.22 03:26 Alexius123456 A raiz de mi post del karaoke

2022.01.22 03:26 DeathOnion Penny Sleeve Damage in Binders?

Is it true that cards can get damaged from moving around penny sleeves in binders, assuming they're not double sleeved? How much of an issue is this actually?