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Elements of Probability

  • Experiment → repeatable process with outcome (such as a coin flip)
  • Sample Space (𝑆) → all possible outcomes ({𝐻,𝑇})
  • Event → subset of sample space (flipping and getting 𝑇)
  • Probability → 𝑃(𝐸)=desired outcomesall outcomes
    • If you roll a D6, the chance of rolling a 4 → 16

Special Events

  • Certain Event → always happens
  • Impossible Event → never happens

Multiplicative Rule (And)

  • The probability that two events both happen

Dependent Probabilities

  • Outcome of one event does effect the other
  • 𝑃(𝐴𝐵)=𝑃(𝐴)×𝑃(𝐵|𝐴)
    • 𝐵|𝐴 → probability of 𝐵 given 𝐴 has happened already

Independent Probabilities

  • Outcome of one event does not effect the other
  • 𝑃(𝐴𝐵)=𝑃(𝐴)×𝑃(𝐵)

Additive Rule (Or)

  • 𝑃(𝐴𝐵)=𝑃(𝐴)+𝑃(𝐵)𝑃(𝐴𝐵)
    • If events are independent, 𝑃(𝐴𝐵)=0

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