Lecture Notes Chapter 2 Sections 2.5 and 2.6

# Lecture Notes Chapter 2 Sections 2.5 and 2.6 -...

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To begin this section, we will be looking at  unemployment data from 1989.  This will lead us  naturally into Conditional Probability.

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Education Employed Unemployed Total Elementary School 5,299 406 5,765 High School, 1-3 years 8,144 705 8,149 High School, 4 years 38,171 1763 39,934 College, 1-3 years 19,991 671 20,662 College, 4+ years 26,015 570 26,585 Total 97,620 4,115 101,735 Civilian Labor Force in the USA, 1989 (Figures in Thousands) A common summary of these data is the “unemployment rate,” which is the Percentage of unemployed workers given by: But this figure does not take into account the educational level.  We would  need to narrow the focus to each row of the above chat.                      This is called  conditioning. ( 29 %. 0 . 4 100 000 , 735 , 101 000 , 115 , 4 =
Here, we see the unemployment rates conditioned  to education. Note the increase from 7% to 8% from Elementary  School to High-School, 1-3 year.  Why do you  think this increase occurred? If you were to poll a person, what is the     probability that person is unemployed                            given that he has graduated from High         School, but has had no College? Education Employed Unemployed Elementary School 93% 7% High School, 1-3 Years 92% 8% High School, 4 years 96% 4% College, 1-3 years 97% 3% College, 4+ years 98% 2% Unemployment rates by Education

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Suppose we look at the following Venn diagram: Suppose event A represents students who receive  an A, and B represents Business Majors. Note that P(A) = 0.1, but what is the probability  that a business major gets an A? There are only 20 business majors, and 3 of them  got A’s.  So the probability that a               business major gets an A is 0.15.
If A and B are any two events, then the  conditional probability   of A given B, denoted by  P(A|B), is         provided P(B) > 0. The definition of conditional probability basically  restricts the sample space down to the event B,  because we already know B has happened.  Thus  we only care about the amount of the event A  which is in B. P(B) P(AB) B) | P(A =

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Example 1:  From among 5 motors, of which one  is defected, two are to be selected at random for  use on a particular day.  Find the probability that  the second motor is non-defective, given that first  was non-defective. Solution:  Let N
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## This note was uploaded on 02/04/2011 for the course MATH 1780 taught by Professor Snyder during the Fall '08 term at North Texas.

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Lecture Notes Chapter 2 Sections 2.5 and 2.6 -...

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