Insurance

actuarial risk assessment and premium tables

A car insurance premium is calculated as (probability of claim) × (average payout) × loading factor. Actuaries spend their whole careers refining these probabilities.

Medicine

clinical trial analysis and drug efficacy statistics

Phase-3 clinical trials report drug efficacy as "drug arm vs placebo arm" probability ratios. The COVID vaccines reported 95% efficacy — a probability statement.

AI / ML

Bayesian inference, probabilistic models, NLP

Every word ChatGPT produces is the next-token sample from a probability distribution over 100k+ candidates. Spam filters use Bayesian probability to detect junk mail.

Finance

options pricing, Value-at-Risk, portfolio theory

Black-Scholes option pricing computes the probability the underlying ends above strike. Value-at-Risk reports the probability of losing more than X over Y days.

Weather

precipitation forecasts and storm probabilities

"70% chance of rain" comes from running 1000s of simulations and counting how many had rain — Monte Carlo probability in production.

Exams

dice, cards, coins problems across all competitive tests

Probability questions on dice, cards, balls and "at least one" complement problems are standard in CAT, GMAT, GRE and every Bank PO paper.