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# More Probability - More Probability Rules and Confidence...

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The General Addition Rule We had the probabilities of two events and then subtract out the probability of their intersection Does not require disjoint events P( A or B) = P (A) + P(B) – P(A and B)
Using the General Addition Rule A survey of college students found that 56% live in campus residence halls, 62% participate in a meal plan and 42% do both. What the probability that a randomly selected student either lives or eat on campus? Let L = student lives on campus Let M= student has a meal plan on campus

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P(a student either lives or eats on campus)= P(L or M) P(L) + P(M) – P(L and M) = .56 + .62 - .42 = .76 There’s a 76% chance that a randomly selected college student either lives or eats on campus
Conditional Probability When we want a conditional probability, we write P(B/A) and pronounce it “the probability of B given A” To find the probability of B given A, we restrict our attention to the outcomes of A and then find the fraction of those outcomes B also occurred ) ( ) ( ) ( A P AandB P A B P =

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Recap: Our survey found that 56% of college students live on campus, 62% have a campus meal plan and 42% do both While dining in a campus facility open only to students with meal plans, you meet someone interesting. What is the probability this person lives on campus? Let L = student lives on campus Let M = student has a campus meal plan
P(student lives on campus and has a meal plan)= = .42/.62 = .677 There is a probability of about .677 that a student with a meal plan lives on campus ) ( ) ( ) ( M P LandM P M L P =

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The General Multiplication Rule What to do when variables are not independent… ) ( ) ( ) ( A B xP A P AandB P =
How to determine independence: Looking back to the multiplication Rules: P(A AND B) = P(A) * P(B) -> when independent -> when they are not independent ) ( ) ( ) ( A B xP A P AandB P =

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Checking for Independence Info: P(L) = .56, P(M) = .62, P(L and M)= .42 Are living on campus and having a meal plan independent? Are they disjoint? If these events are independent, then knowing that a student lives on campus doesn’t affect the probability that she has a meal plan Check if ) ( ) ( B P A B P =
P(M/L) = .42/.56 = .75 P(M) = .62 Because .75 does not equal .62, the events are not independent, students who live on campus are more likely to have meal plans. Living on campus and having a meal plan are not disjoint either; in fact, 42% do both ) ( ) ( M P L M P = ) ( ) ( ) ( L P MandL P L M P =

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Independent vs. Disjoint
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## This note was uploaded on 01/09/2010 for the course ILRST 2100 at Cornell University (Engineering School).

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More Probability - More Probability Rules and Confidence...

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