1 / 13

Probability Formulae

Probability Formulae. Chapter 10 Probability Formulae. Look over the formulae under the first 3 headings. This is assumed knowledge. We are going to go through the rest of the formulae in the next two lessons. . A. B. Mutually Exclusive Events.

akamu
Download Presentation

Probability Formulae

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 Formulae

  2. Chapter 10 Probability Formulae Look over the formulae under the first 3 headings. This is assumed knowledge. We are going to go through the rest of the formulae in the next two lessons.

  3. A B Mutually Exclusive Events If two or more events cannot occur simultaneously they are said to be mutually exclusive. On a Venn Diagram mutually exclusive events show up as separate sets so n(A  B) = 0 Pr(A  B) = 0

  4. Identifying Mutually Exclusive Events Method 1: Use commons sense to see if the events can happen together if they can’t they are mutually exclusive

  5. Identifying Mutually Exclusive Events Method 2: Check the following formulae Pr(A  B) = 0 Pr(A  B) = Pr(A) + Pr(B)

  6. Using the mutually exclusive rule Example 1 If A and B are mutually exclusive what is the probability of A or B happening if Pr(A) = 0.3, Pr(B) = 0.2? Pr(A or B) = Pr(AB) Since mutually exclusive Pr(AB) = Pr(A) + Pr(B) Pr(AB) = 0.3 + 0.2 Pr(AB) = 0.5

  7. Testing for mutual exclusivity Example 2 Are A and B mutually exclusive if Pr(A) = 0.4, Pr(B) = 0.5 and Pr(AB) = 0.9 ? Pr(A  B) = 0.9 Pr(A) + Pr(B) = 0.4 + 0.5 = 0.9 since Pr(A B) = Pr(A) + Pr(B) the events aremutually exclusive

  8. Testing for mutual exclusivity Example 3 Are A and B mutually exclusive if Pr(A) = 0.1, Pr(B) = 0.4 and Pr(AB) = 0.7 ? Pr(AB) = 0.7 Pr(A) + Pr(B) = 0.1 + 0.4 = 0.5 since Pr(AB)  Pr(A) + Pr(B) the events are notmutually exclusive

  9. The General Probability Rule Pr(A  B) = Pr(A) + Pr(B) – Pr(A  B)

  10. Using The General Probability Rule Example 1 What is Pr(A  B), if Pr(A) = 0.6, Pr(B) = 0.2 and Pr(A  B) = 0.1 ? Pr(A  B) = Pr(A) + Pr(B) – Pr(A  B) Pr(A  B) = 0.6 + 0.2 – 0.1 Pr(A  B) = 0.7

  11. Using The General Probability Rule Example 2 What is Pr(A B), if Pr(A) = 0.6, Pr(B) = 0.8 and Pr(A  B) = 0.9 ? Pr(A  B) = Pr(A) + Pr(B) – Pr(A  B) 0.9 = 0.6 + 0.8 – Pr(A  B) 0.9 = 1.4 – Pr(A  B) -0.5 = - Pr(A  B) 0.5 = Pr(A  B)

  12. Using The General Probability Rule Example 3 Use the General Probability Rule to find Pr(A  B), if Pr(A) = 0.3, Pr(B) = 0.4 and A and B are mutually exclusive? Since mutually exclusive Pr(A  B) = 0 Pr(A  B) = Pr(A) + Pr(B) – Pr(A  B) Pr(A  B) = 0.3 + 0.4 – 0 Pr(A  B) = 0.7 Same as using the Mutually Exclusive Rule

  13. Exercise Work through the questions on the Using the Mutually Exclusive & General Probability Formulaeworksheet

More Related