The Birthday Problem

Think you know stats? Let’s have some fun. [The Rude Awakening] June 09, 2023 [WEBSITE]( | [UNSUBSCRIBE]( The Birthday Problem - Beyond the simple mathematics lie statistics. - But are we really good at stats? - Let’s look at this issue that’s vexed the stats community since it was proven. [Insider Reveals A Breakthrough New Way To Profit From AI]( Do not… I repeat… [Do NOT buy any AI stocks until you watch this short video in full.]( [Click here to learn more]( You’re about to discover a breakthrough new way to profit from the rise of AI that has never been revealed before. the types of companies we target with this strategy have shown top-performing gains like 1,167% in 11 days, 1,779% in 13 days and even 2,900% in just 3 days. Starting with $5,000, that’d be enough to walk away with profits like $63,350, $93,950 and $150,000 – all in a matter of days. But you must hurry… (As this is time sensitive). [Click here now for details on this new AI strategy.]( [Click Here To Learn More]( [Sean Ring] SEAN RING Happy Friday from the Big Orange! We’ve been suffering the Canadian wildfire haze this week, but that hasn’t dampened our spirits. The class I’ve been teaching with bosom bud Andy has gone well. The kids are from an absolute smorgasbord of the best schools in America. We’ve got Harvard, Michigan, Washington University in St. Louis, Penn State, Colorado, Colorado State, and my trusty alma mater, Villanova, among others. And they’re really sweet young people, as well. Andy was teaching about data and statistics when I chipped in with my favorite statistics problem. It blew their minds, as it did mine when I first learned about it. Since my mathy Rudes seem to go over well, I thought I’d share it with you. The Question When I interjected in Andy’s class (with his permission, of course), I asked one question: What is the probability that at least two of you have the same birthday? To be clear, we’re just looking for day and month, not year. So my birthday is December 20, 1974. We’d consider December 20, 1990, a match because we’re not looking at the year. There are 229 students, 2 teachers, and five bank support staff in the room for a total of 236 people. Now if you never heard of this famous problem before, you may offer something like “1 in a million” like I did. It’s not even close to the correct answer, as you’ll see. To their great credit, the kids didn’t offer any outlandish answers like I did. Most guesses were from “very low” to “50%” to “63%” to “very high” and “above 90%.” I was impressed. But the answer is 99.99999%. Don’t believe it? I’ll prove it to you. The Birthday Problem Explained Before I show you the math, let me tell you what happened in class. After I asked the question and got those very good answers, I said, “Now, let’s have some fun.” I then asked, “Who has a January birthday?” About 25 people raised their hands. Then and there, I knew we’d have a match. I pointed to a young intern, and asked, “What date were you born on?” “January 17th,” she replied. “Any of you with your hands up born on the 17th?” I asked. One of the other interns had his hand up. The class clapped uproariously. I said, “Wow! The rabbit came out of my hat on the first try!” The kids marveled. Since I already knew the math, I wasn’t surprised at all. [Over 62 And Collect Social Security? Take Action Immediately!]( [Click here to learn more]( [If you’re over the age of 62 and currently collect Social Security, you need to prepare now](. Because Biden has given our country the worst inflation in decades – and many warn things will only get worse from here. Worse yet, the Social Security check you receive now may not keep pace with inflation… [Which is why, if you don’t act now, you could fall behind in the months ahead](. Is your retirement at immediate risk? [Click here now to get the simple, step-by-step actions to survive inflation](. [Click Here To Learn More]( The Math Behind The Birthday Problem Alright, let's dive deeper into the math behind the Birthday Problem. Don't worry, I promise it won't be as daunting as it sounds! The probability is easier to calculate if we consider the opposite: what is the probability that all people in a group have different birthdays? First, consider an empty room and the first person who walks in. The probability that their birthday is not shared with anyone else (since they're alone) is 100% or 365 out of 365. Now, the second person who comes in can have any of the remaining 364 days as their birthday to not share it with the first person. So the probability for the second person is 364 out of 365. As the third person enters, they must avoid the two existing birthdays, so their probability is 363 out of 365. As you continue this process, the probabilities keep declining for each new person. So, for a group of 23 people, you'd multiply these individual probabilities together: Let P = Probability. P(all different) = (365/365) x (364/365) x (363/365) x ... x (343/365) This comes out to around 0.4927, or a 49.27% chance that all 23 people have different birthdays. But remember, we want the probability that at least two people share a birthday. So, we subtract the "all different" probability from 1: P(at least one shared) = 1 - P(all different) = 1 - 0.4927 = 0.5073, or 50.73% So, surprisingly, in a group of just 23 people, there's over a 50% chance that at least two people share the same birthday! This is the surprising and counter-intuitive result that makes the Birthday Problem so fascinating. For you traders out there, this means “take the bet” if there are 23 people in the room. By the time we get to 57 people, the chances are just over 99% that two people will have the same birthday. So with over 230 people in the room, the call was a no-brainer. Here’s a chart of the Birthday Problem outcomes: [SJN] Credit: Sean Ring I knew of the Birthday Problem because I read a book called Chance, by Amir Aczel, a long time ago. Aczel was a statistics professor who wrote that little book because he was so frustrated at the innumeracy displayed daily. [I share his opinion](. Aczel dedicated an entire chapter to the Birthday Problem because it’s so counterintuitive, even statisticians have trouble with it. So don’t fret if you’re still trying to understand it. Professional mathematicians are still trying to understand it. But more than that, it’s a reminder to not use our guts when it comes to financial decision-making. It’s important to think of the statistics behind our choices. Wrap Up Today’s short Rude is a reminder we don’t know it all, and we may never will. But that’s okay because every advantage acquired brings us closer to the life we want. Just being aware of this paradox puts you in a special club. May knowing this increase your intellectual curiosity and eagerness to learn. Have a wonderful and restful weekend! All the best, [Sean Ring] Sean Ring Editor, Rude Awakening Twitter: [@seaniechaos]( In Case You Missed It… Oh, Rats! NYC, We Have a Problem! [Sean Ring] SEAN RING Good morning Reader, Greetings from the home of the rat race run daily, New York City. This week, I’m here teaching interns at one of the big US banks. It’s a short three-day program, so I’ll be back home Saturday morning. You’d think after the government-mandated private sector shutdown of 2020-2021, New York’s biggest problem would be to get people to come back. But they have, to a certain extent. I still think my Paradigm colleague James Altucher is right, rather than Seinfeld, in that NYC’s heyday is long gone. My problem is that I’m anchored in Giuliani-era New York. I graduated in 1996 from Villanova, so I came to NYC when it was Disneyified. Note: “Disneyfied” in the 1990s meant “cleaned up,” rather than its 2020s meaning of “turned to crap.” Examples: 1996: “Oh my God! Times Square has been Disneyfied! It’s so clean compared to the 80s!” 2023: “Oh my God! Kathleen Kennedy Disneyfied Star Wars! Now no one wants to watch it!” I can’t believe I’m writing about rat infestations in major cities. But teaching last year in NYC blew me away. So far, nothing this year has changed my mind. Last August in NYC I spent a full month in New York last July and August teaching graduate programs for two of the megabanks here. I hadn’t been back in years, and I was keen to see my colleagues, so I enthusiastically accepted the assignment. We were staying Downtown, so I thought my British and Irish colleagues would enjoy a drink at Fraunces’ Tavern. That’s where George Washington announced he’d resigned his commission and would return to civilian life. Shortly before noon that day, Washington assembled about thirty soldiers to the Long Room at Fraunces Tavern for his last goodbye. There is only one known complete account of this event, [written by Colonel Benjamin Tallmadge](. In his 1830 memoir, he recounts: “We had been assembled but a few moments when his excellency entered the room. After partaking of a slight refreshment in an almost breathless silence the General filled his glass with wine and turning to the officers said, “With a heart full of love and gratitude I now take leave of you. I most devoutly wish that your latter days may be as prosperous and happy as your former ones have been glorious and honorable.” After the officers had taken a glass of wine General Washington said, “I cannot come to each of you but shall feel obliged if each of you will come and take me by the hand.” General Knox, the closest officer to Washington, walked up to the General and the two hugged and kissed with tears running down their faces. Tallmadge recalls, “In the same affectionate manner every officer in the room marched up and parted with the general in chief. Such a scene of sorrow and weeping I had never before witnessed and fondly hope I may never be called to witness again.” It’s a wonderful pub, with a museum attached. I thought it’d be a great idea to drink over our shared history. We noticed there were open seats in front of the pub on the street. As it was a glorious night, we thought we’d sit outside and enjoy it. Little did we know we were encroaching on claimed territory. Not five minutes after we sat, the rats came out in full force. No joke… these rats were running from one sewer hole to another, with the route running under our chairs. It was positively revolting! We ran back inside to finish our drinks and then hightailed it out of there. I’m sure it’s not Fraunces’ fault. It’s crap city management. That opinion was confirmed when NYC Mayor and Chief of Uselessness Eric Adams appointed a “rat czar.” [US Attack on Nord Stream a Covert “Act of War”?]( [Click here to learn more]( In this shocking presentation, new evidence reveals the TRUTH about the attack on Nord Stream, and why millions of Americans would be devastated from the fallout. [See for yourself.]( [Click Here To Learn More]( What’s a Director of Rodent Migration? I guess we don’t hate the Russians so much to stop using the term “czar.” But if the unions only let innovation have its way, we’d probably not need one. For instance, when I was in Florence earlier this year, I noticed the Florentines innovated their trash stash and collection. It was so cool! [trash removal in Florence] Credit: Sean Ring Basically, the garbage cans are attached to the top of a huge underground trash box. When it’s time to collect the garbage, the garbage truck lifts up the box by the can with a crane. Then the trap door underneath opens and the trash goes into the truck. No garbagemen! Now that’s innovation. Alas, NYC doesn’t innovate in such ways. So Mayor Adams appointed Kathleen Corradi as New York City’s first-ever director of “rodent mitigation.” From [The New York Times]( Ms. Corradi is not a trained rodentologist. A former elementary school teacher, she developed the city’s Zero Waste Schools initiative while at the Education Department and led the agency’s rodent reduction efforts. She will oversee the city’s existing army of rat experts. The city’s Department of Health and Mental Hygiene already has a rodent biologist on staff, the renowned urban rodentologist Robert Corrigan, who has been busy installing movement sensors on city streets to monitor rat behavior. The health department also has an Office of Pest Control, and there is a citywide rodent task force. Mr. Adams said Ms. Corradi will connect those bodies with agencies like the Department of Sanitation, in a concerted push to help battle some of the city’s longest-tenured and most notorious residents. “You’ll be seeing a lot of me and a lot less rats,” said Ms. Corradi, who will be paid $155,000 a year. I can think of a lot of places where $155,000 could go. But we wouldn’t want a repeat of The Black Death, would we? The Black Death of 1347-1350 Rats played a significant role in the spread of the Black Death, the devastating pandemic that occurred in Europe between 1347 and 1350. Also known as the Bubonic Plague, the bacterium Yersinia pestis caused it. The primary carriers of Yersinia pestis are fleas that infest rats, specifically, the species known as the black rat (Rattus rattus) and the brown rat (Rattus norvegicus). During the Middle Ages, these rat species were commonly found in cities and towns throughout Europe. The transmission of the disease occurred in the following way: fleas would infest rats and feed on their blood, ingesting the Yersinia pestis bacteria. When infected rats died, fleas would seek new hosts, including humans. When a flea bit an infected rat and then bit a human, it transmitted the bacteria into the person's bloodstream. The dense rat populations in urban areas, combined with unsanitary living conditions, provided the perfect environment for the rapid spread of the disease. Rats would infest homes, streets, and markets, bringing infected fleas into close proximity to humans. Additionally, rats' tendency to travel on ships facilitated the spread of the disease between different regions. The Black Death devastated Europe, with an estimated 25 to 50 million deaths during the epidemic. The disease spread quickly, causing high mortality rates and significant social and economic disruptions. It would take Europe centuries to recover. Besides our historical lesson, there are some very real reasons to keep the rats at bay. The Genuine Dangers of an Out-of-Control Rat Population Let’s face it. We children of the modern and postmodern eras have merely thought trash laying around is “disgusting” or “ugly.” It’s rare to have the prescience to think it’s a health hazard. After all, we haven’t had to worry about that for a good, long while. Sewage systems and trash collection were invented a long time ago. And it was working just fine up until recently. So let’s refresh ourselves on why an out-of-control rat population is a real danger: - Health Hazards: Rats are carriers of various diseases transmitted to humans. They spread bacteria, viruses, and parasites through their droppings, urine, and bites. Some of the diseases associated with rats include leptospirosis, salmonellosis, hantavirus, rat-bite fever, and plague. These diseases cause severe illness and death. - Property Damage: Rats have strong teeth that continually grow, leading them to gnaw on various objects to control the length of their teeth. They cause significant damage to buildings, infrastructure, electrical wiring, and pipes. Chewed wires result in electrical fires, and structural damage weakens buildings, posing risks to occupants. - Contamination of Food Sources: Rats are notorious for contaminating food supplies in storage facilities, warehouses, restaurants, and homes. They can chew through packaging, leave droppings and urine on food items, and spread pathogens. This contamination poses a significant risk to public health, leading to foodborne illnesses. - Damage to Agricultural Areas: Rats are awful for agricultural areas surrounding cities. They destroy crops, feed on stored grain, and damage farm equipment. This results in losses for farmers, lower availability, and lower affordability of food. - Negative Impact on Tourism and Business: A city plagued by a severe rat infestation suffers from a damaged reputation. The presence of rats in public spaces, restaurants, or hotels deter tourists and visitors. Additionally, businesses lose financially because of rate damage and the subsequent expenses to fix the problem. - Ecological Disruption: Rats have adverse effects on local ecosystems. They prey on native bird eggs and compete with other small mammals for resources, disrupting the balance of local wildlife. This leads to a biodiversity decline. Wrap Up Only in America? Nah, it could happen anywhere with pisspoor government oversight. I wonder if Mayor Adams even thought of privatizing garbage collection. Why not? It would almost certainly be better than this government service. But more than that, rampant rats dent NYC’s reputation and keep people away. And no big city can afford that post-government-mandated private-sector shutdown. Let me know what you think by emailing me [here](mailto:feedback@dailyreckoning.com). Have a good rest of your week! All the best, [Sean Ring] Sean Ring Contributing Editor, The Morning Reckoning feedback@dailyreckoning.com Twitter: [@seaniechaos]( [Paradigm]( ☰ ⊗ [ARCHIVE]( [ABOUT]( [Contact Us]( © 2023 Paradigm Press, LLC. 808 Saint Paul Street, Baltimore MD 21202. By submitting your email address, you consent to Paradigm Press, LLC. delivering daily email issues and advertisements. To end your Rude Awakening e-mail subscription and associated external offers sent from Rude Awakening, feel free to [click here.]( Please note: the mailbox associated with this email address is not monitored, so do not reply to this message. We welcome comments or suggestions at feedback@rudeawakening.info. This address is for feedback only. 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