Markov Chains: The Strange Math Behind Google, ChatGPT & Nuclear Bombs | Zetsapp
Independence means knowing the result of event A tells you nothing about event B. In formal probability: P(B|A) = P(B). This makes calculations tractable because you can just multiply probabilities. P(two heads) = P(head) × P(head) = 0.5 × 0.5 = 0.25. Once you have dependence, you need conditional probabilities, and the math gets much harder — which is exactly why Bernoulli and others assumed independence, and exactly why Markov's willingness to tackle the dependent case was so significant.