Assume 15% of the world\'s population has a certain genetic condition. A blood t

Question

Assume 15% of the world's population has a certain genetic condition. A blood test for the condition is available, but it is not 100% accurate. For those who do not have the genetic condition, the blood test will return a positive result 6% of the time Additionally, for those who have the genetic condition, the test returns a negative result 7% of the time Note: A "positive" result means the test indicates that the individual has the condition; a "gtive" result means the test indicates that the individual does not have the condition. Since the test, however, is not 100% accurate, an indication that an individual has or does not have the condition doesn't necessarily mean the individual actually has or does not have the condition Download the following Excel spreadsheet by clicking the following words in bold: Download Excel File Define the event C1 to be the event that a randomly selected person has the genetic condition. Likewise, define the event C2 to be the event that a randomly selected person does not have the genetic condition. Notice that the events C1 and C2 are mutually exclusive. Finally, define the event T as the event that the blood test returns a positive result. You will use the Excel worksheet you downloaded to conduct a tabular approach to Bayes' theorem calculations. You will select the values you compute in the following sample worksheet. Prior Conditional Joint Posterior 2 Events Probabilities Probabilities Probabilities Probabilities P(Ci) P(CinT) P(C I T) 4 Enter the prior probabilities P(C1) into cell B4 and P(C2) into cell B5 of your downloaded Excel worksheet and select these same values in the sample worksheet. Enter the conditional probabilities P(T C1) into cell C4 and P(T I C2) into cell C5 of your downloaded Excel worksheet and select these same values in the sample worksheet The conditional probability P(T | C1) represents the probability given In cells D4 and DS of the Excel worksheet, compute the joint probabilities P(C1 nT) and P(C2 nT). Select the values you obtain in the sample worksheet. Finally, in cells E4 and E5 of the Excel worksheet, compute the posterior probabilities P(CT) and P(C2 I T). Select the values you obtain in the sample worksheet. The probability of a positive test result is If a randomly selected person has a positive test result, the probability that he or she does not have the condition is

Explanation / Answer

from above information:

P(C1) =0.15 : P(C2) =1-0.15 =0.85

P(T|C1) =1-P( of negative test given condition) =1-0.07 =0.93

P(T|C2) =0.06

P(C1nT) =P(C1)*P(T|C1) =0.1395

P(C2nT) =P(C2)*P(T|C2) =0.051

P(T) =P(C1nT)+P(C2nT) =0.1905

P(C1|T) =P(C1nT)/P(T)= 0.7323

P(C2|T) =P(C2nT)/P(T)= 0.2677

P(T|C1) represent the probability of hving genetic condition given test returns a positive resut.

probability of a positive test is P(T)=0.1905

she does not have the condition is =P(C2|T) =0.2677

P(Ci) P(T|Ci) P(CinT) P(Ci|T) C1 0.15 0.93 0.1395 0.732283 C2 0.85 0.06 0.051 0.267717

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