1 / 23

Probability

Probability. Terminology. Example: genders (Boy, Girl) of a two-child family. In this example, P(BB) = ¼ = 0.25 or 25%. Classical Probability : When each (simple) event in the sample space is equally likely to occur, then the probability of any event A occurring (“ P(A) ”) is ….

quincy
Download Presentation

Probability

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

  2. Terminology

  3. Example: genders (Boy, Girl) of a two-child family In this example, P(BB) = ¼ = 0.25 or 25%. Classical Probability: When each (simple) event in the sample space is equally likely to occur, then the probability of any event A occurring (“P(A)”) is …

  4. Sequential or non-sequential outcomes The probability of first getting a boy, and then a girl, is P(BG) = ¼ =0.25 or 25%. But the probability of having = 2/4 = 0.50 or 50%.

  5. Example: A parts inspector finds the parts either defective (D) or non-defective (N). Three parts are inspected in sequence. What is the probability that the inspector will find at least two defective items? A = {DDD, DDN, DND, NDD} and P(A) = 4/8 = 0.50 or 50%

  6. Relative Frequency or Empirical Probability Before a coin flip experiment, if we are going to flip a coin, we say that the probability of heads P(H) = ½. However, looking backwards in time, if we repeat the experiment several times, the relative frequency or empirical probability can be defined as For example, if we’ve flipped a coin 10 times and gotten 4 heads, the empirical probability of a heads is P(A) = 4/10 = 40%.

  7. * (12 + 18)/(60+75) = 0.22.

  8. Law of Large Numbers: states that as the number of experimental trials is increased, the relative frequency will converge toward the (true) probability. Computer simulation on a coin toss 200 times. Computer simulation on a coin toss 1,000 times.

  9. Basic Laws of Probability

  10. A compound event is the combination of two or more events.

  11. White area: Only A (not B) White area: Only B (not A) Blue area: Both A and B

  12. Mutually Exclusive Events: If A, then not B; If B, then not A (no common events)

  13. Addition Rule (more generally)

  14. From previous example:

  15. Conditional Probability: The probability that an event will occur, given that another event has occurred.

  16. From previous example:

  17. Dependent and Independent Events If having knowledge of one event does not affect the probability of occurrence of another event, the two events are said to be independent. Example: If males and females get the same grades, on average, then the probability of a student getting an “A”, given that the student is a female, is the same as the probability of a (any) student getting an “A”. P(“A” | female) = P(“A”)

  18. Equation (1) * Multiply both sides of Equation (1) by P(M) and switching sides gives P(G∩M) = P(G|M) x P(M). But if the two events are independent, then P( G|M) = P(G). By substitution, P(G∩M) = P(G) x P(M).

  19. Problem/Solution: Find P(G), P(N), P(B∩N) and P(B|N)

More Related