Defining Probability

Probability measures the likelihood of events, ranging from 0 to 1. It originated from analyzing games of chance and has evolved into a critical tool in various fields such as finance, science, and philosophy.Probability vs. Odds

While often used interchangeably, probability and odds convey different information. Probability reflects the chance of occurrence, whereas odds compare the likelihood of an event occurring to it not occurring.Conditional Probability

Conditional probability assesses the chance of an event given that another is already known to occur. It's vital in Bayesian statistics, updating beliefs with new evidence.Law of Large Numbers

This law posits that as a sample size grows, its mean gets closer to the average of the whole population. It underpins the stability of long-term insurance and finance predictions.Monty Hall Problem

A famous probability puzzle where switching doors after a reveal increases winning chances. Initially counterintuitive, it's a classic example of conditional probability's practical implications.Zero Probability Events

Events with zero probability may still be possible; for example, picking an exact real number from a continuous distribution. It highlights probability's nuance beyond just 'impossible' or 'certain'.Quantum Probability

Beyond classical interpretation, quantum mechanics introduces probability fields, where particles exist in superposition states, challenging our macroscopic understanding of chance.What does probability measure?

Likelihood of events 0 to 1

Comparison of non-occurring events

Prediction of exact outcomes

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