1 / 11

6.3: General Probability Rules

6.3: General Probability Rules. The Rules So Far. 1. Probabilities are between 0 and 1 for any event A 2. The sum of all probs for a given sample space is 1 3. P(A c ) = 1 – P(A) 4. Addition Rule for Disjoint events P(A or B) = P(A) + P(B) 5. Multiplication Rule for Independent Events

kaceyg
Download Presentation

6.3: General Probability Rules

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. 6.3: General Probability Rules

  2. The Rules So Far • 1. Probabilities are between 0 and 1 for any event A • 2. The sum of all probs for a given sample space is 1 • 3. P(Ac) = 1 – P(A) • 4. Addition Rule for Disjoint events • P(A or B) = P(A) + P(B) • 5. Multiplication Rule for Independent Events • P(A and B) = P(A)P(B)

  3. Union: Definition and Rule • The Union of a collection of events is the event that at least one of the collection of events occurs • The Addition Rule for Disjoint Events: P(At least one occurrence happening from the set of events) = P(A) + P(B) + P(C) + …AS LONG AS THE EVENTS ARE DISJOINT!! (Sorry. Didn’t mean to shout.)

  4. The Addition Rule for Any two events, Disjoint or not • P(A or B) = P(A) + P(B) – P(A and B) or • P(A  B) = P(A) + P(B) – P(A  B)

  5. Disjoint, yes? • P(A or B) = P(A) + P(B) A B

  6. A B Disjoint? No! • Now P(A or B) = P(A) + P(B) – P(A  B) A  B !!

  7. A B • Why subtract P(A  B)? That overlap area (now orange) is covering up another area just like it in green. To gauge the true total area properly, we must throw one of them away! A  B !!

  8. A B So—In general: • P(A or B) = P(A) + P(B) – P(A  B)

  9. Example: Dartmouth/Cornell • George believes he has a .4 change of being accepted at Dartmouth, and a .3 chance of being accepted at Cornell. • Furthermore, he thinks he has a .2 chance of being accepted at both. • What is the probability of being accepted at either one? Dartmouth or Cornell?

  10. Dartmouth/Cornell • P(D or C) = P(D) + P(C) – P(D and C) • P(D  C) = P(D) + P(C) – P(D  C) P(D  C) = .4 + .3 - .2 = .5

  11. .1 Dartmouth/Cornell • Or, adding the areas, P(Dartmouth or Cornell) = .2 + .2 + .1 = .5 .2 .2 .

More Related