statistics

statistics - Classic Probability Theory number of favorable...

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Classic Probability Theory Classic Probability Theory number of favorable outcomes number of favorable outcomes total number of possible outcomes total number of possible outcomes P(A) = P(A) = If A and B are independent events [occurrence of one has no effect upon the occurrence of the other]: P(A and B) = P(AB) = P(A)P(B) P(A and B) = P(AB) = P(A)P(B) probability of flipping two coins and having both come up heads: 0.5*0.5 = 0.25, 25% chance P(AB) = 0 P(AB) = 0 when A and B are mutually exclusive probability of a single coin flip resulting in both heads and tails…. . 1. Probability of A and B occurrence [joint probability]:

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1. Probability of A or B occurrence: for mutually exclusive events, P(A+B) = P(A) + P(B) P(A+B) = P(A) + P(B) probability of one club or one spade chosen in one draw from a deck of cards = 13/52 + 13/52 = 0.5 For non-mutually-exclusive events, P(A+B) = P(A) + P(B) – P(A+B) = P(A) + P(B) – P(AB) P(AB) avoids “double-counting probability of drawing either an ace or a spade on a given draw from a deck of cards = 4/52 [an ace] + 13/52 [a spade] – 1/52 [the ace of spades] = 0.3077
1. Conditional probability: probability of an event conditional upon occurrence of another event…. ) ( ) ( ) ( B P AB P B A P = = ) ( B A P probability that A will occur given that B has occurred ) ( ) ( ) ( A P AB P A B P = ) ( ) ( ) ( ) ( ) ( A P A B P B P B A P AB P = =

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17,000 7,000 10,000 15,950 6,250 9,700 Acceptable 1,050 750 300 Defective total Vendor 2 Vendor 1 Let: • A 1 = event “part from vendor 1” • A 2 = event “part from vendor 2” • B 1 = event “acceptable part” • B 2 = event “defective part” event “acceptable part from vendor 1 acceptable/defective parts from vendors 1 and 2 acceptable/defective parts from vendors 1 and 2 = 1 1 A B
59 . 0 17000 10000 ) ( 1 = = A P and a few calculations…. and a few calculations…. 41 . 0 17000 7000 ) ( 2 = = A P 97 . 0 10000 9700 ) ( 1 1 = = A B P 11 . 0 7000 750 ) ( 2 2 = = A B P 03 . 0 10000 300 ) ( 1 2 = = A B P 89 . 0 7000 6250 ) ( 2 1 = = A B P Question: What is the probability of selecting a single part that is made by vendor 1 and is also defective? 018 . 0 03 . 0 * 59 . 0 ) ( ) ( ) ( ) ( 1 2 1 1 2 2 1 = = = = A B P A P A B P B A P

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In a particular village, there are 60 women and 40 men. Twenty of those women are 70 years of age or older; 5 of the men are 70 years of age or older. Example 2 [Cliffs Quick Review of Statistics] Example 2 [Cliffs Quick Review of Statistics] What is the probability that a person selected at random in that town will be a woman? P(A P(A 1 ) = 60/100 = 0.60 ) = 60/100 = 0.60 What is the probability that a person 70+ years of age selected at random will be a woman? = 20/25= 0.80 = 20/25= 0.80 • A 1 = event “woman” • A 2 = event “man” • B 1 = event “woman, 70 or older” • B 2 = event “man, 70 or older” = 2 1 A B event “70 or older and woman ****************************************************** ) B A P( 1 1
What is the probability that a person selected from the village population will be a woman, 70 years of age or older? Finally…. . Finally…. . 2 . 0 ) 60 / 20 ( * 60 . 0 ) ( * ) ( ) ( ) ( 1 1 1 1 1 1 1 = = = = A B P A P A B P B A P

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Probability Distributions – the Binomial Probability Distributions – the Binomial experiment consists of a number of identical events (n) each event has only one of two mutually exclusive outcomes [“success” or “failure”]
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statistics - Classic Probability Theory number of favorable...

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