Foundations of Quality Management and Strategic Decision Making

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Foundations of Quality Management and Strategic Decision Making Let is the event that a randomly selected individual has the rare form of the cancer. Let is the event that the diagnostic test results in positive to that rare form of the cancer. Then express the D E ( ) ( ) ( ) ( ) ( ) given information in terms of the probabilities of the events and , Pr 0.25% 0.0025 Pr 1 Pr 1 0.0025 0.9975 Pr | 98% 0.98 Pr | 2% 0.02 a. The probability that a person chosen at random from this D E r D D D E D E D = =  = − = − = = =  = = ( ) ( ) ( ) ( ) ( )   ( )( ) ( )( ) population will test positive is, Pr Pr | Pr Pr | Pr By total probability rule 0.98 0.0025 0.02 0.9975 0.0224 b. If a person chosen at random tests positive, the probability that the person in E E D D E D D   = + = + = ( ) ( ) ( ) ( ) ( ) ( ) ( )   ( )( ) ( )( ) ( )( ) fact has the cancer is, Pr | Pr Pr | By Baye's theorem Pr | Pr Pr | Pr 0.98 0.0025 0.98 0.0025 0.02 0.9975 0.00245 0.0224 0.1094 E D D D E E D D E D D =   + = + = =
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