According to Science Daily, researchers have developed a new non-invasive technique which can accurately detect malignant melanoma

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 2.1% 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 9.1% 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!
€‹a. 0.021
b. 0.979
c. 1.000
d. 0.000
e. 0.091
f. 0.909
g. 0.021
h. 0.000
i. 0.089
j. 0.890

Determine the probability that someone who tests positive actually has cancer. Show all work using the equation editor. PLEASE use 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.