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Understanding Probability: Classical, Frequency & Subjective Approaches

Learn about classical, frequency, and subjective approaches to probability, mutually exclusive events, addition rule, complementary events, marginal & conditional probabilities, independent events, multiplication rule, probability trees, discrete & continuous distributions, cumulative distribution function, and expected values.

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Understanding Probability: Classical, Frequency & Subjective Approaches

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  1. Introduction to Probability

  2. Approaches to probability • The classical approach • The relative frequency approach • The subjective approach

  3. Mutually exclusive events Two events are mutually exclusive (or disjoint) if the occurrence of one of the events precludes the simultaneous occurrence of the other

  4. The addition rule • If A and B are mutually exclusive events: • p(A or B) = p(A) + p(b) • If A and B are not mutually exclusive: p(A or B) = p(A) + p(b) –p(A and B)

  5. Complementary events

  6. Marginal probabilities p(worker contracts cancer) = 268/1000 = 0.268

  7. Conditional probabilities p(worker contracts cancer | exposed tochemical) = 220/355 = 0.620

  8. Independent events If two events, A and B, are independent: p(A | B) = p(A)

  9. The multiplication rule If A and B are independent events: p(A and B) = p(A) p(B) If A and B are not independent: p(A and B) = p(A) p(B | A)

  10. Probability trees

  11. Discrete probability distribution

  12. Continuous probability distribution

  13. Cumulative distribution function

  14. Expected values

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