7. On the basis of a physical examination and symptoms, a physician as- sesses the probabilities that the patient has no tumour, a benign tumour, or a malignant tumour as 0.70, 0.20, and 0.10, respectively. A thermographic test is subsequently given to the patient. This test gives a negative result with probability 0.90 if there is no tumour, with probability 0.80 if there is a benign tumour, and with probability 0.20 if there is a malignant tumour. a) What is the probability that a thermographic test will give a negative result for this patient? b) Obtain the posterior probability distribution for the patient when the test result is negative? c) Obtain the posterior probability distribution for the patient when the test result is positive? d) How does the information provided by the test in the two cases change the physician's view as to whether the patient has a malignant tumour?
7. On the basis of a physical examination and symptoms, a physician as- sesses the probabilities that the patient has no tumour, a benign tumour, or a malignant tumour as 0.70, 0.20, and 0.10, respectively. A thermographic test is subsequently given to the patient. This test gives a negative result with probability 0.90 if there is no tumour, with probability 0.80 if there is a benign tumour, and with probability 0.20 if there is a malignant tumour. a) What is the probability that a thermographic test will give a negative result for this patient? b) Obtain the posterior probability distribution for the patient when the test result is negative? c) Obtain the posterior probability distribution for the patient when the test result is positive? d) How does the information provided by the test in the two cases change the physician's view as to whether the patient has a malignant tumour?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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In the textbook(or article):STATISTICS FOR ECONOMISTS: A BEGINNING in toronto university. I don' understand bayes theorem. How solve this 4 question?
Transcribed Image Text:7. On the basis of a physical examination and symptoms, a physician as-
sesses the probabilities that the patient has no tumour, a benign tumour, or
a malignant tumour as 0.70, 0.20, and 0.10, respectively. A thermographic
test is subsequently given to the patient. This test gives a negative result
with probability 0.90 if there is no tumour, with probability 0.80 if there is
a benign tumour, and with probability 0.20 if there is a malignant tumour.
a) What is the probability that a thermographic test will give a negative
result for this patient?
b) Obtain the posterior probability distribution for the patient when the
test result is negative?
c) Obtain the posterior probability distribution for the patient when the
test result is positive?
d) How does the information provided by the test in the two cases change
the physician's view as to whether the patient has a malignant tumour?
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