Lct03a - Introduction to Business Statistics Lecture 3A...

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1 Introduction to Business Statistics Lecture 3A Conditional Probability and Statistical Independence Example ( Sex Discrimination ): A company of 1200 employees (960 men and 240 women) promoted 288 men and 36 women last year. Is a man more likely to be promoted than a woman? Is a promoted person more likely to be a man? Is there a ground to claim sex discrimination? Let us first find the probability “the randomly selected employee was promoted last year on the condition that the employee is male” Let T be the event that the selected employee was promoted last year and M be the event that the selected employee is male. Then we write the conditional probability as P ( T | M )
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2 z Conditional probability is the revised proportion based on the subpopulation (a different sample space). z What is the size of male subpopulation? (960) In the subpopulation how many were promoted? (288) So the revised proportion is 288/960 = 0.3. z The other way to find the conditional probability is through the following definition using probabilities in the original sample space. 3 . 0 8 . 0 24 . 0 1200 / 960 1200 / 288 ) ( ) M ( ) | ( = = = = M P T P M T P ; 15 . 0 2
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Lct03a - Introduction to Business Statistics Lecture 3A...

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