This is my second time posting this question because part 2 was not answered. Ac

Question

This is my second time posting this question because part 2 was not answered.

According to Science Daily, researchers have developed a new non-invasive technique which can accurately detect malignant melanoma without a biopsy. In their lifetimes 1.9% of Americans will develop malignant melanoma. The new test will correctly identify melanoma in 100% of cases where it is present, but gives a positive result in 7.4% of cases where it is not. Fill in the correct values in your tree diagram below. Each value should be carried out to three decimal places as appropriate. Don't forget your leading zero!

Part 1 of 2: B Fill in the values below to complete the tree diagram. Write each solution to three decimal places (including a leading zero).

a.

b.

c.

d.

e.

f.

g.

h.

i.

j.

Part 2 of 2: Determine the probability that someone who tests positive actually has cancer. Show all work using the equation editor. Then comment (using complete sentences) on whether this test is a good alternative to biopsies. Be sure to use the appropriate probability notation at the beginning of your work and show all work using the values from your tree diagram in the equation editor.

Positive POCancer n Positive) g Test Malignant Melanoma Negative n Negative) 3h POCancer Test Positive PONo cancer n Positive) i Test A No Skin Cancer Negative PONo cancer n Negative) j Test

Explanation / Answer

Solution :-

This question will be solved using Bayes theorem,

Part 1 :-

a. 0.019

b. 0.981

c. 1

d. 0

e. 0.074

f. 0.926

g. 0.019

h. 0

i. 0.072594

j. 0.908406

Part 2.

P (someone who tests positive actually has cancer) = ?

When we substitute the known probabilities into Bayes rule, we get the results

Substituting the value in the equation we get,

P(someone who tests positive actually has cancer) = 0.2074

This test is a good alternative to biopsies, as it has got good accuracy in detection of cancer when it is present.

P( Ak | B ) = P( Ak B ) / {P( A1 B ) + P( A2 B ) + . . . + P( An B )}

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.