According to Science Daily, researchers have developed a new mo invasive techniq

Question

According to Science Daily, researchers have developed a new mo invasive technique which can accurately detect malignant melanoma without a biopsy, their lifetimes 2.4% of Americans will develop malignant melanoma. The new test will correctly identify new test melanoma in 97% of cases where it is present, but Rives a positive result in 6.5 % of cases where it not. Fill n 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!

Explanation / Answer

(a)

From the graph we have

P(cancer) = 0.024

(b)

By the complement rule

P(No cancer) = 1 - P(cancer) = 1- 0.024 = 0.976

(c)

P(Positive|Cancer) = 0.97

(d)

By the complement rule

P(Negative|Cancer) = 1 - P(Positve | Cancer) = 1 - 0.97 = 0.03

(e)

P(Positive|No Cancer) = 0.065

(f)

By the complement rule

P(Negative|No Cancer) = 1 - P(Positve | No Cancer) = 1 - 0.065 = 0.935

(g)

P(Positive and Cancer) = P(Positive|Cancer) P(Cancer) = 0.97 * 0.024 = 0.02328

That is P(Positive and Cancer) = 0.023

(h)

P(Negative and Cancer) = P(Negative|Cancer) P(Cancer) = 0.03 * 0.024 = 0.00072

That is P(Negative and Cancer) = 0.001

(i)

P(Positive and No Cancer) = P(Positive|No Cancer) P(No Cancer) = 0.065 *0.976= 0.06344

That is P(Positive and no Cancer) = 0.063

(j)

P(Negative and no Cancer) = P(Negative|No Cancer) P(No Cancer) = 0.935 * 0.976 = 0.913

That is P(Negative and no Cancer) = 0.913

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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