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Probability Concepts

Probability Concepts. Language Notes:. One die. A deck of cards (52 total). Hearts Clubs Spades Diamonds. Four suits. Two or more dice. Probability Limits. Types of Probabilities.

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Probability Concepts

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  1. Probability Concepts Language Notes: One die A deck of cards (52 total) HeartsClubs SpadesDiamonds Four suits Two or more dice

  2. Probability Limits

  3. Types of Probabilities Note: These types of probabilities are known as “marginal” or “simple” probabilities because they look at a single event in isolation of anything else.

  4. Event Types

  5. Adding Events

  6. (Non-) Exclusivity Visually P(spade) = 13/52 P(five) = 4/52 P(seven) = 4/52 These two events are mutually exclusive, so they don’t overlap. P(five and Spade) = 1/52 These two events are NOT mutually exclusive. Example: Cards P(5 or Spade) = 4/52 + 13/52 – 1/52 = 16/52 = 4/13

  7. Statistically (In)dependent Events

  8. Conditional Probabilities A conditional probability is the probability of a second event B occurring given that a first event A has occurred. P(B|A) When events are independent, the value of the conditional and simple probabilities are the same. Only when independent: P(B|A) = P(B)

  9. Statistical (In)dependence

  10. Causality Sometimes, the direction of causality is clear and obvious; other times it is not. Are people poorer because the live upcountry?... • Do people steal because they are poor?... Or are people poor because they steal? Or do people move upcountry because they are poor? Or, is there another factor – e.g. their character – that causes them to be both poor and a thief?

  11. Probability of Independent Events * P(A and B) is written P(AB) Example: when rolling a die two times, the probability of rolling a 6 on the first try and a 1 on the second try = 1/6 x 1/6 = 1/36

  12. Probability of Dependent Events When two events are dependent, the joint probability of both events happening requires using the conditional probability of the dependent event: Recall that when events B and A are independent: P(AB) = P(B)P(A) Also note that we can rewrite the second equation as: P(B|A) = P(AB)/P(A) This is the formula for calculating conditional probabilities. When event B is dependent on event A: P(AB) = P(B|A)P(A) Note that these two equations are the same only when P(B) = P(B|A), which is the earlier definition of independence.

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