Probability

Key people

• Gotthilf HagenGerman physicist (1797–1884)
• David George KendallBritish statistician (1918–2007)
• Philippe FlajoletFrench computer scientist (1948–2011)
• Ronen EldanIsraeli mathematician and theoretical physicist

Timeline

• 1810Further proofs were given by Laplace (1810, 1812), Gauss (1823), James Ivory (1825, 1826), Hagen (1837), Friedrich Bessel (1838), W.F.
• 1844Donkin (1844, 1856), and Morgan Crofton (1870).

Read

• A first course in probabilitySheldon M. Ross · 1976Book
• An introduction to probability theory and its applicationsWilliam Feller · 1950Book
• Introduction to Probability and StatisticsWilliam Mendenhall · 1967Book
• Introduction to probability modelsSheldon M. Ross · 1972Book

Watch

• Math Antics - Basic ProbabilitymathanticsVideo
• Statistics And Probability | Overview Of Random Variable & Probability DistributionDr.Gajendra PurohitVideo
• Introduction to Probability, Basic Overview - Sample Space, & Tree DiagramsThe Organic Chemistry TutorVideo

Listen

• The Probability DeskUniversal Asset OwnersPodcast
• ProbabilityAshutosh DubeyPodcast
• Probability MattersProbability MattersPodcast
• STATISTICS AND PROBABILITYELMARIE MABANSAYPodcast

Voices to follow

• Josefine Lindström@Jossan_L_ · XSwedish analyst and journalist
• Pau Sisternas Fajardo@pau_s_f · XResearcher
• Fredrik Lindsten@LindstenFredrik · XStatistician

Debates

• Is probability an objective property of the world or a measure of our knowledge?One view: Probability is an objective frequency of events over many trials, existing independently of our minds (Frequentist view). · Another: Probability reflects our subjective belief or degree of certainty about an event, updated with new evidence (Bayesian view).Open question
• Is true randomness possible, or is everything ultimately deterministic?One view: True randomness exists in quantum mechanics and chaotic systems, meaning outcomes are fundamentally unpredictable. · Another: All events, including seemingly random ones, are determined by prior causes, even if too complex for us to predict.Open question

Glossary

• ProbabilityA numerical measure of the likelihood that an event will occur, ranging from 0 (impossible) to 1 (certain).
• EventA specific outcome or a set of outcomes from a random experiment.
• Sample SpaceThe set of all possible outcomes of a random experiment.
• Random VariableA variable whose value is a numerical outcome of a random phenomenon.
• Conditional ProbabilityThe probability of an event occurring given that another event has already occurred.
• Expected ValueThe average value of a random variable over a large number of trials.

Careers

Roles this can lead toward

Threads 15

Where this connects to other fields — and why it's worth knowing.

• Does God Exist? Philosophy

  Pascal said: bet that God exists. If you're right, the reward is infinite; if you're wrong, you lose almost nothing. Even if the odds are tiny, a tiny chance times an infinite payoff still wins the bet. That weird 'multiply the payoff by the odds' move is exactly how casinos and insurance companies price everything today.

• Natural Hazards and Disaster Geography Geography

  Insurance exists because people needed to put a price on rare disasters, the once-in-a-century flood or quake. Figuring out the odds of those freak events forced people to invent the math of 'tail risk,' the rare-but-huge stuff. Now climate change is making those disasters so frequent that the math breaks and some places can't be insured at all.

• Political Philosophy Philosophy

  Philosopher John Rawls asked: design the rules of society before you know who you'll be, rich or poor, healthy or sick, behind a 'veil of ignorance.' You'd build a fair world because you might land at the bottom. That's really just buying insurance: you protect against every version of yourself, because you don't know which one you'll get.

• Planetary Boundaries Environment

  Why build a fence far back from a cliff edge instead of right at it? Because thick fog hides exactly where the edge really is. Scientists set 'planetary boundaries' the same way, giving Earth a wide safety margin, not because we'll fall at the line, but because nobody knows precisely where the true danger point sits.

• Cyber & Critical Infrastructure Global Risks

  Insurance works because car crashes are independent; yours doesn't cause your neighbor's, so payouts average out. Cyberattacks break that. One computer worm can hit millions of customers on the same day at once. When everyone fails together, the 'safety in numbers' that insurance depends on collapses, which is why cyber is so hard to insure.

• Climate Migration and Habitability Geography

  The first people to flee a climate danger zone aren't residents; they're insurance companies. Their number-crunchers quietly raise prices or refuse to cover flood-prone areas, pulling money out before a single family packs up. So the cold math of risk is the earliest warning sign that a place is becoming unlivable.

• Extreme Weather Environment

  The first group to give up on a flooding coastline isn't the government, it's the insurance company. When they decide a place is too risky to insure, the math nerds who calculate risk have basically declared it unlivable, long before anyone official says so.

• The Trolley Problem Philosophy

  The trolley problem asks if you'd sacrifice one life to save five. Governments actually answer this in spreadsheets, putting a dollar price on a human life. That number decides how many deaths a safety rule is allowed to prevent.

• Stoicism Philosophy

  A smart gambler judges a bet by whether it was a good call, not by whether it happened to win. Ancient Stoics did the same with life: imagine what could go wrong, then focus on deciding well, not on the result. Both are really the art of choosing when you can't know the outcome.

• Work, Automation & the Gig Economy Economics

  A regular job hands the boss the risk: you get the same paycheck and sick pay even in a slow week. Gig work like driving or delivery flips that, so a bad week is your problem alone. What gets sold to you as 'be your own boss, work when you want' is really the company handing you all the uncertainty it used to absorb.

• The Search for Alien Life Science

  There's a famous equation that guesses how many alien civilizations might be out there by multiplying a bunch of maybes together. If life is common, though, the silent sky becomes a warning: something keeps wiping civilizations out, a 'Great Filter,' and it might be a disaster still ahead of us, not behind.

• AI in Medicine Health

  Imagine a test that's 99% accurate for a disease only 1 in 10,000 people have. Run it on everyone and most "positive" results are false alarms. AI diagnostics do this at massive scale, tripping over the same math trap as always.

• Nuclear Energy Technology

  No private insurance company will cover a full nuclear meltdown, because the worst case is too catastrophic to price. So nuclear power only exists because governments agree to absorb that giant risk. That refusal to insure is the honest measure of how dangerous a meltdown really is.

• Startup Funding Business

  Startup investing isn't a bell curve where most bets land near average. It's a world where one giant 100x winner pays for ninety-nine total flops. So the usual advice to "spread out to stay safe" is backwards here; you're hunting for the rare monster win.

• Genetic Engineering & CRISPR Health

  Insurance works because nobody knows exactly who'll get sick, so everyone chips in and shares the risk. But once companies can read your DNA, they can price you by your personal odds. That knowledge quietly breaks the shared gamble that makes insurance possible.