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Elements of Probability

  • Experiment โ†’ repeatable process with outcome (such as a coin flip)
  • Sample Space (๐‘†) โ†’ all possible outcomes ({๐ป,๐‘‡})
  • Event โ†’ subset of sample space (flipping and getting ๐‘‡)
  • Probability โ†’ ๐‘ƒ(๐ธ)=desired outcomesall outcomes
    • If you roll a D6, the chance of rolling a 4 โ†’ 16

Special Events

  • Certain Event โ†’ always happens
  • Impossible Event โ†’ never happens

Multiplicative Rule (And)

  • The probability that two events both happen

Dependent Probabilities

  • Outcome of one event does effect the other
  • ๐‘ƒ(๐ดโˆฉ๐ต)=๐‘ƒ(๐ด)ร—๐‘ƒ(๐ต|๐ด)
    • ๐ต|๐ด โ†’ probability of ๐ต given ๐ด has happened already

Independent Probabilities

  • Outcome of one event does not effect the other
  • ๐‘ƒ(๐ดโˆฉ๐ต)=๐‘ƒ(๐ด)ร—๐‘ƒ(๐ต)

Additive Rule (Or)

  • ๐‘ƒ(๐ดโˆช๐ต)=๐‘ƒ(๐ด)+๐‘ƒ(๐ต)โˆ’๐‘ƒ(๐ดโˆฉ๐ต)
    • If events are independent, ๐‘ƒ(๐ดโˆฉ๐ต)=0

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