According to Science Daily, researchers have developed a new non-invasive techni

Question

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.

Explanation / Answer

Solution:-

a = Probability of having Melignant Melanoma = 1.9/100 = 0.019

b = Probability of not having Melignant Melanoma = 1 - 0.019 = 0.981

c = Chances of detecting Melignant Melanoma when it is present = 100/100 = 1

d = Chances of not detecting Melignant Melanoma when it is present = 0

e = Chances of giving positive result where it is not = 7.4/100 = 0.074

f = Chances of giving negative result where it is not = 1 - 0.074 = 0.926

g = Probability of detecting Melignant Melanoma when it is present = 1 × 0.019 = 0.019

h = Probability of not detecting Melignant Melanoma when it is present = 0 × 0.019 = 0.00

i = Probability of giving positive result where it is not = 0.074 × 0.981 = 0.073

j = Probability of giving negative result where it is not = 0.926 × 0.981 = 0.908

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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