1 / 12

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.

len
Télécharger la présentation

Probability Concepts

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related