i need step by step answer 4.108 A screening test for a certain disease is prone

Question

i need step by step answer

4.108 A screening test for a certain disease is prone to giving false positives or false negatives. If a patient being tested has the disease, the probability that the test indicates a (false) negative is.13. If the patient does not have the disease, the probability that the test indicates a (false) positive is .10. Assume that 3% of the patients being tested actually have the disease. Suppose that one patient is chosen at random and tested. Find the probability that: (Hint: Use a tree diagram. When drawing your diagram, consider the first stage to be whether or not the patient has the disease, and let the second stage be results of the test a. this patient has the disease and tests positive b. this patient does not have the disease and tests positive c. this patient tests positive (Hint: A tree diagram may be helpful in part c.) d. this patient has the disease given that he or she tests positive

Explanation / Answer

The four stages are

a) Disease and Test positive- 0.03*0.87=0.0261

2) Disease and Tests negative- 0.03*0.13

b) NoDIsease and Test positive=0.97*0.10=0.097

4) Nodisease and test negative-0.97*0.90

c)P( positive) = 0.097+0.0261= 0.1231

d)P( Disease/Positive)=0.0261/0.1231=0.2120

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