a) P(mole is cancerous) = P(positive test result/mole is cancerous)= P(negative

Question

a)

P(mole is cancerous) =

P(positive test result/mole is cancerous)=

P(negative test result/mole is bengin)=

b) If the bio-electrical test is positive for cancer, what is the probability that this mole is actually cancerous? Show work and it may be helpful to make a tree diagram or taple.

5. Swedish engineers developed a minimally invasive method for detecting skin cancer using bio-electrical impedance spectra. Their method achieved a 96% sensitivity and86% specificity when tested on skin moles that were known to be cancerous or known to be benign (non-cancerous), respectively. Suppose this test is done for a patient with a suspicious-looking mole. Prior to testing, the chance that such a mole is cancerous is 40% a) The following probabilities are given in the statement above. Give the specific values for each of these probabilities. Hint: No calculations are needed and none are helpful. [1 point each]

Explanation / Answer

Ans:

a)

P(mole is cancerous) =0.40

P(positive test result/mole is cancerous)=0.96

P(negative test result/mole is bengin)=0.86

sensitivity is the ability of a test to correctly identify those with the disease (true positive rate)

specificity is the ability of the test to correctly identify those without the disease (true negative rate).

b)P(positive)=0.96*0.4+(1-0.86)*(1-0.4)=0.468

P(cancereous/positive)=P(positive/cancereous)*P(cancereous)/P(positive)  

=0.96*0.4/0.468

=0.821

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