9. The prostate-specific antigen (PSA) test is a blood test used to screen for p
ID: 3073837 • Letter: 9
Question
9. The prostate-specific antigen (PSA) test is a blood test used to screen for prostate cancer. Elevated PSA levels are often associated with prostrate cancer, but they can also reflect other conditions. A positive PSA test does not necessarily indicate prostate cancer, and not all cases of prostate cancer can be detected by a PSA test. A pamphlet published by the health insurance company Kaiser Permanente includes the clever diagram shown to the right to represent the possible outcomes of a PSA test with their respective frequencies a) Use this diagram to find the probabilities of a true positive, a false positive, a false negative, and a true negative. b) What is the positive predictive value of the PSA test? In other words, find the conditional probability that a randomly selected man has prostate cancer given that he receives a positive test result. A gardener plants seeds for three types of flowers (A, B, and C), with 48% of the seeds for type A, 32% for type B, and the remaining 20% for type C. It is known that 90% of the seeds for type A will germinate. 30% of the seeds for type B will germinate, and 60% of the seeds for type C will germinate. Use this information to draw a tree diagram, and then use your tree diagram to answer the following questions a) What is the probability that a randomly selected seed is for type A and germinates? b) What is the probability that a randomly selected seed is for type C and does not germinate? c) What percent of all of the planted seeds will germinate? d) What is the probabality that a seed that germinates is for type A? e) What is the probability that a seed is either for type B or does not germinate? 1) What is the probabality that a seed that does not germinate is for type B 10Explanation / Answer
Answer to question# 9)
Given:
True positive = 3
False positive = 7
False negative = 1
True negative = 89
.
Answer to part a)
P(true positive) = 3/100 = 0.03
P(False positive) = 7/100 = 0.07
P(False negative) = 1/100 = 0.01
P(True negative) = 89/100 = 0.89
.
Answer to part b)
Positive predictive value = true positive / true poisitve + false positive
Positive predictive value = 3 /(3+7) = 3/10 = 0.3
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