DONE Chapter 13 Notes - General Rules of Probability.docx - STAT 1450 COURSE NOTES CHAPTER 13 GENERAL RULES OF PROBABILITY Guided Notes associated with

DONE Chapter 13 Notes - General Rules of Probability.docx -...

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S TAT 1450 C OURSE N OTES – C HAPTER 13 G ENERAL R ULES OF P ROBABILITY Guided Notes associated with the Lecture Video for Sections 13.1&13.2 Connecting Chapter 13 to our Current Knowledge of Statistics Probability theory leads us from data collection to inference. The introduction to probability from Chapter 12 will now be fortified by additional rules to allow us to consider multiple types of events. The rules of probability will allow us to develop models so that we can generalize from our (properly collected) sample to our population of interest. 13.1 Independence and the Multiplication Rule Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. Thus, if A and B are independent , P(A AND B) = P(A) x P(B) Example: Someone with type O-negative blood is considered to be a “universal donor.” According to the American Association of Blood Banks, 39% of people are type O-negative. Two unrelated people are selected at random. Calculate the probability that both have type O- negative blood. We can apply the concept of independence. P(both type o negative blood) = P (first type o-) x P (second type 0 negative) (.39)(.39) = .1521 Chapter 13, page  1
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13.2 The General Addition Rule Two-Way tables are helpful ways to picture two events. Venn diagrams are an alternative means of displaying multiple events. Both can be used to answer many questions involving probabilities. Example: In a sample of 1000 people, 88.7% of them were right-hand dominant, 47.5% of them were female, and 42.5% of them were female and right-hand dominant. Draw a Venn diagram for this situation. Calculate the probability that a randomly selected person is right-hand dominant or female. 1 st method: .462 +.425 + .050 =.937 Let R =right hand dominant (.887) and let F= female (.475) 2 ND METHOD: .887+ .475 -.425 = .937 this is actually = P(R) + P(F) – P(RAND F)= P(R OR F) We just used the general addition rule: For any two events A and B , P( A OR B) = P(A) – P(A AND B) Question: Where did we see this concept previously? OR” questions from Chapter 6 where two events “overlapped.” What if the two events A and B do not overlap? Events A and B are DISJOINT if they have no outcomes in common. Question: What is P ( A or B ) when A and B are disjoint?
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