IndependenceConditioning

IndependenceConditioning - Le arning Obje s ctive fine De...

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Learning Objectives Define conditional probability Calculate conditional probabilities for discrete events (e.g., coin tosses). Define independence
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Example Suppose that two doctors test all patients coming into a blood donation center for anemia. Suppose that the first doctor diagnoses 10% of all patients as positive, the second doctor diagnoses 17% of all the patients as positive, and both doctors diagnose 8% of all patients as positive. What is the conditional probability that the second doctor makes a positive diagnosis of anemia given that the first doctor makes a negative diagnosis?
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Conditional Probability Reason based on partial information Conditional probability of A given B P ( A | B )
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Example Roll a fair six-sided di P( outcome is 6 ) = 1/6
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Example Roll a fair six-sided di What is P(outcome is 6| outcome is even)? P( | ) = outcome is even outcome is 6 1/3
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Conditional Probability Conditional probability of A given B P ( A | B ) = P ( A B ) P ( B ) P ( A | B ) = P ( A B ) P ( B ) = 1 6 3 6 = 1 3
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Example Roll two fair 6-sided dice A = both show the same number P( A ) = 6 / 36
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Example Roll two fair 6-sided dice B = their sum is not greater than 3 P( B ) = 3 / 36
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Example A = both show the same number B = their sum is not greater than 3 P( A B ) = 1 / 36
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This note was uploaded on 02/22/2010 for the course BME 335 taught by Professor Dunn during the Spring '10 term at University of Texas at Austin.

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IndependenceConditioning - Le arning Obje s ctive fine De...

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