PHIL 125 Practice 5
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2/16/24, 9:06 PM E1 Practice 5 Medical tests and Bayes: PHIL 125 003 2023W2 Introduction to Scientific Reasoning E1 Practice 5 Medical tests and Bayes Due Feb 9 at 11:59p.m. Points 11 Questions 11 Time Limit None Attempt History Attempt Time Score LATEST Attempt 1 59 minutes 11 out of 11 () Correct answers are hidden. Score for this quiz: 11 out of 11 Submitted Feb 9 at 11:27p.m. This attempt took 59 minutes. Question 1 1/ 1 pts The ELISA test is used to screen donated blood for the presence _ ofthe AIDS virus. The test WOrkS prior-prob(Member_blood_HIV+) x Pred-prob(Elisa_test_blood_"HIV+" IF Member_blood_HIV+) by finding antibodies to the virus. When the virus is present, the ELISA test finds antibodies and [ Prior-prob(Member_blood_HIV+) x Pred-prob(Elisa_test_blood_"HIV+" IF Member_blood_HIV+)| so is positive with a probability of + | Prior-prob(Member_blood_HIV-) x Pred-prob(Elisa_test_blood_"HIV+” IF Member_blood_HIV-)| 0.897. When the virus isn't present the test sometimes still finds antibodies and gives a positive result. This happens With pyjr_prob(Member_blood_HIV+) x Pred-prob(Elisa_test_blood_"HIV-" IF Member_blood_HIV+) a probability of 0.015. Suppose the true infection rate for blood donated by members | Prior-prob(Member_blood_HIV+) x Pred-prob(Elisa_test_blood_"HIV-" IF Member_blood_HIV+)| of a par[icu|ar group IS 19%. + [H’ior-prob(Member_blood_HIV -)x Pred-prob(Elisa_nest_blood_"I'IIV M IF l\fiember_blood_H]V -)J Post-prob(Member_blood_HIV+ IF Elisa_test_blood_"HIV+") Post-prob(Member_blood_HIV+ IF Elisa_test_blood_"HIV-") According to the information given in the problem what is the prior probability that a randomly selected group member's donated blood is HIV+? 1% 99% 99.7% 0.3% 1.5% https://canvas.ubc.ca/courses/132235/quizzes/708094 1/8
2/16/24, 9:06 PM E1 Practice 5 Medical tests and Bayes: PHIL 125 003 2023W2 Introduction to Scientific Reasoning 98.5% Question 2 1/1 pts The ELISA test is used to screen donated blood for the presence _ of the AIDS virus. The test WOrkS prjor-prob(Member_blood_HIV+) x Pred-prob(Elisa_test_blood_"HIV+" IF Member_blood_HIV+) by finding antibodies to the virus. When the virus is present, the ELISA test finds antibodies and [Prior-prob(Member_blood_HIV+) x Pred-prob(Elisa_test_blood_"HIV+" IF Member_blood_HIV+)] SO is positive with a probability of + | Prior-prob(Member_blood_HIV-) x Pred-prob(Elisa_test_blood_"HIV+” IF Member_blood_HIV-)| 0.997. When the virus isn't present the test sometimes still finds antibodies and gives a _ positive result. This happens Wit pyjr_prob(Member_blood_HIV+) x Pred-prob(Elisa_test_blood_"HIV-" IF Member_blood_HIV+) a probability of 0.015. Suppose the true infection rate for blood donated by members | Prior-prob(Member_blood_HIV+) x Pred-prob(Elisa_test_blood_"HIV-" IF Member_blood_HIV+)| of a particular group is 1%. + | Prior-prob(Member_blood_HIV-) x Pred-prob(Elisa_test_blood_"HIV-" IF Member_blood_HIV-)| Post-prob(Member_blood_HIV+ IF Elisa_test_blood_"HIV+") Post-prob(Member_blood_HIV+ IF Elisa_test_blood_"HIV-") According to the information given in the problem what is the prediction probability that a randomly selected sample of blood which is HIV+ will test negative on the ELISA test? 1% 99% 99.7% 0.3% 1.5% 98.5% Question 3 1/1 pts The ELISA test is used to screen donated blood for the presence _ of the AIDS virus. The test works Prior-prob(Member_blood_HIV+) x Pred-prob(Elisa_test_blood_"HIV+” IF Member_blood_HIV+) by finding antibodies to the virus. When the virus is present, the ELISA test finds antibodies and | Prior-prob(Member_blood_HIV+) x Pred-prob(Elisa_test_blood_"HIV+” IF Member_blood_HIV+)| SO is positive with a probability of + | Prior-prob(Member_blood_HIV-) x Pred-prob(Elisa_test_blood_"HIV+” IF Member_blood_HIV-)| 0.997. When the virus isn't present the test sometimes still finds antibodies and gives a _ positive result. This happens With - pyj or_prob(Member_blood_HIV+) x Pred-prob(Elisa_test_blood_"HIV-" IF Member_blood_HIV+) a probability of 0.015. Suppose the true infection rate for blood donated by members | Prior-prob(Member_blood_HIV+) x Pred-prob(Elisa_test_blood_"HIV-" IF Member_blood_HIV+)]| of a particular group is 1%. + | Prior-prob(Member_blood_HIV-) x Pred-prob(Elisa_test_blood_"HIV-" IF Member_blood_HIV-)| Post-prob(Member_blood_HIV+ IF Elisa_test_blood_"HIV+") Post-prob(Member_blood_HIV+ IF Elisa_test_blood_"HIV-") https://canvas.ubc.ca/courses/132235/quizzes/708094 2/8
2/16/24, 9:06 PM E1 Practice 5 Medical tests and Bayes: PHIL 125 003 2023W2 Introduction to Scientific Reasoning Suppose the Elisa test comes out negative for a particular group member's donated blood. Based on the information given in the problem what is the posterior result probability that it is infected with HIV -- that is, it's HIV+? (Answers have been rounded to 1 decimal place.) 40.2% 59.8% 100.0% 0.0% 0.3% Question 4 1/1 pts A few years ago Washington DC started a screening program for HIV infecttion. The program's goal is to screen every resident aged 18 to 84 using the Oraquick test. The Oraquick test has a true positive rate for HIV of 94% and a true negative rate of 9%%. Washington DC has an estimated population of 600,000. According to the information given in the problem what is the prediction probability that a randomly Post-prob(Popn_member_HIV+ IF OraQuick_test "HIV+”) Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test "HIV+” IF Popn_member_HIV+) | Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test_"HIV+” IF Popn_member_HIV+)| + | Prior-prob(Popn_member_HIV-) x Pred-prob(OraQuick_test "HIV+” IF Popn_member_HIV-)| Post-prob(Popn_member_HIV+ IF OraQuick_test "HIV-") Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test "HIV-" IF Popn_member_HIV+) | Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test_"HIV-" IF Popn_member_HIV+)| + | Prior-prob(Popn_member_HIV-) x Pred-prob(OraQuick_test "HIV-" IF Popn_member_HIV-)| selected person who is HIV- will test positive on the OraQuick test? 94% 6% 99% 1% Question 5 1/1 pts https://canvas.ubc.ca/courses/132235/quizzes/708094 3/8
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2/16/24, 9:06 PM E1 Practice 5 Medical tests and Bayes: PHIL 125 003 2023W2 Introduction to Scientific Reasoning A few years ago Post-prob(Popn_member_HIV+ IF OraQuick_test "HIV+”) Washington DC starteda ~ ’ , . screening program for Hy - Frior-prob(Popn_member HIV+) x Fred-prob(OraQuick_test "HIV+" IF Popn_member_HIV+) infecttion. The program's goal s 1o screen every | Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test_"HIV+” IF Popn_member_HIV+)| resident aged 18 to 84 + | Prior-prob(Popn_member_HIV-) x Pred-prob(OraQuick_test "HIV+” IF Popn_member_HIV-)| using the Oraquick test The Oraquick test has a true positive rate for HIV of Post-prob(Popn_member_HIV+ IF OraQuick_test "HIV-") 94% and a frue negative < _ . rate of 99% Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test "HIV-" IF Popn_member_HIV+) Washington DC has an eslimated population of | Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test_"HIV-" IF Popn_member_HIV+)] 600,000. + | Prior-prob(Popn_member_HIV-) x Pred-prob(OraQuick_test "HIV-" IF Popn_member_HIV-)| It is estimated that on average 1 in 50 people living in Washington DC are HIV+. This does not mean that they know it. Suppose a person from DC takes the OraQuick test and the test comes out positive. Based on the information given in the problem and the general rate of HIV infection what is the posterior result probability that a randomly selected member of the DC population is infected with HIV -- that is, is HIV+? (Answers have been rounded to 0 decimal places.) 66% 34% 100% 0% 94% Question 6 1/1 pts Suppose you have a patient who Post-prob(Popn_member_HIV+ IF OraQuick_test "HIV+") belongs to a population with a high HIV- infection rate. 1 in every 4 people in this Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test_"HIV+” IF Popn_member_HIV+) population have the infection. To either confirm or disconfirm the infection you give the patient an | Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test "HIV+” IF Popn_member_HIV+)| + | Prior-prob(Popn_member_HIV-) x Pred-prob(OraQuick_test "HIV+” IF Popn_member_HIV-)| OraQuick test. The best estimate of this test's accuracy is that it has a true positive rate of 93.5% and a false positive rate of Post-prab(Popn_member_HIV+ IF OraQuick_test "HIV-") 0.5%. - - - o You administer the test by swabbing the Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test "HIV-" IF Popn_member_HIV+) patient's gums. You attend to another patient while waiting for the result. You return 20 minutes later to read the test | Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test "HIV-" IF Popn_member_HIV+)| outcome. + | Prior-prob(Popn_member_HIV-) x Pred-prob(OraQuick_test "HIV-" IF Popn_member_HIV-)] https://canvas.ubc.ca/courses/132235/quizzes/708094 4/8
2/16/24, 9:06 PM E1 Practice 5 Medical tests and Bayes: PHIL 125 003 2023W2 Introduction to Scientific Reasoning According to the information given in the problem, based on the patient being a randomly selected member of a special high-risk population, what is the prior probability that he or she is HIV-? 25% 75% 93.5% 0.5% Question 7 1/1 pts Suppose you have a patient who Post-prob(Popn_member_HIV+ IF OraQuick_test "HIV+") belongs to a population with a high HIV- = infection rate. 1 in every 4 people in this Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test_"HIV+" IF Popn_member_HIV+) population have the infection. To either confirm or disconfirm the infection you give the patient an | Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test "HIV+” IF Popn_member_HIV+)| + | Prior-prob(Popn_member_HIV-) x Pred-prob(OraQuick_test_"HIV+” IF Popn_member_HIV-)| OraQuick test. The best estimate of this test's accuracy is that it has a true positive rate of 935% and a false positive rate of pyg ol (Popn_member HIV+ IF OraQuick_test "HIV-") 05%. - - - o You administer the test by swabbing the Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test_"HIV-" IF Popn_member_HIV+) patient's gums. You attend to another patient while waiting for the result. You return 20 minutes later to read the test | Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test "HIV-" IF Popn_member_HIV+)] outcome. + | Prior-prob(Popn_member_HIV-) x Pred-prob(OraQuick_test "HIV-" IF Popn_member_HIV-)| According to the information given in the problem what is the prediction probability that a randomly selected person who is HIV- will test negative on the OraQuick test? 93.5% 6.5% 99.5% 0.5% Question 8 1/1 pts https://canvas.ubc.ca/courses/132235/quizzes/708094 5/8
2/16/24, 9:06 PM Suppose you have a patient who belongs to a population with a high HIV- infection rate. 1 in every 4 people in this population have the infection. To either confirm or disconfirm the infection you give the patient an OraQuick test. The best estimate of this test's accuracy is that it has a true positive rate of 93.5% and a false positive rate of 0.5%. You administer the test by swabbing the patient's gums. You attend to another patient while waiting for the result. You return 20 minutes later to read the test outcome. E1 Practice 5 Medical tests and Bayes: PHIL 125 003 2023W2 Introduction to Scientific Reasoning Post-prob(Popn_member_HIV+ IF OraQuick_test "HIV+") Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test_"HIV+” IF Popn_member_HIV+) | Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test "HIV+” IF Popn_member_HIV+)| + | Prior-prob(Popn_member_HIV-) x Pred-prob(OraQuick_test "HIV+” IF Popn_member_HIV-)| Post-prob(Popn_member_HIV+ IF OraQuick_test "HIV-") Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test_"HIV-" IF Popn_member_HIV+) | Prior-prob(Popn_member_HIV+) x Pred-prob(OraQuick_test "HIV-" IF Popn_member_HIV+)| + | Prior-prob(Popn_member_HIV-) x Pred-prob(OraQuick_test "HIV-" IF Popn_member_HIV-)] Suppose the OraQuick test turns out to be negative for HIV. What is the chance that the patient is HIV-, considering both the particular population he or she belongs to and the given accuracy rate of the test? (Answers have been rounded to 0 decimal places.) 98% 2% 100% Question 9 1/1 pts Physicians often use two diagnostic tests to determine whether a woman has breast cancer. These are the mammography and the ultrasound test. The results of the two tests are independent of one another. f a woman has breast cancer a positive result on one test doesn't increase or decrease the chance of a positive result on the other test. If a woman doesn't have breast cancer the result on one test doesn't affect the chance of a postive or negative result on the other test. The incidence rate of breast cancer for women at age 40 or older is 1%. ff a woman in this age group has breast cancer the probability is 80% that she will have a positive mammography result. f she doesn't have breast cancer there is still a 10% chance that she will get a positive mammogram. ff a woman 40 or older has breast cancer the chance is 95% that she will have a positive ultrasound test result. On the other hand, if she doesn't have cancer the probability that a woman will have a positive ultrasound result is 4%. Post-prob(Woman=40_BreastCancer+ IF Woman_Mammogram+) Prior-prob(Woman=40_BreastCancer+) x Pred-prob(Woman_Mammogram+ IF Woman=>40_BreastCancer+) [Prior-prob(Woman>40_BreastCancer+) x Pred-prob(Woman_Mammogram+ IF Woman>40_BreastCancer+)] + [Prior-prob(Woman240_BreastCancer-) x Pred-prob(Woman_Mammogram+ IF Woman240_BreastCancer-)] Post-prob(Woman>40_BreastCancer+ IF Woman_Ultrasound+) Prior-prob(Woman>40_BreastCancer+) x Pred-prob(Woman_Ultrasound+ IF Woman240_BreastCancer+) [Prior-prob(Woman>40_BreastCancer+) x Pred-prob(Woman_Ultrasound+ IF Woman>40_BreastCancer+)] + [Prior-prob(Woman>40_BreastCancer-) x Pred-prob(Woman_Ultrasound+ IF Woman>40_BreastCancer-)] According to the information given in the problem what is the prior or pre-test probability that a randomly selected woman over 40 years old has breast cancer? 1% 80% https://canvas.ubc.ca/courses/132235/quizzes/708094 6/8
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2/16/24, 9:06 PM E1 Practice 5 Medical tests and Bayes: PHIL 125 003 2023W2 Introduction to Scientific Reasoning 10% 95% 4% Question 10 1/1 pts Physicians often use two diagnostic tests to determine whether a woman has breast cancer. These are the mammography and the ultrasound test. The results of the two tests are independent of one another. f a woman has breast cancer a positive result on one test doesn't increase or decrease the chance of a positive result on the other test. If a woman doesn't have breast cancer the result on one test doesn't affect the chance of a postive or negative result on the other test. The incidence rate of breast cancer for women at age 40 or older is 1%. ff a woman in this age group has breast cancer the probability is 80% that she will have a positive mammography result. f she doesn't have breast cancer there is still a 10% chance that she will get a positive mammogram. ff a woman 40 or older has breast cancer the chance is 95% that she will have a positive ultrasound test result. On the other hand, if she doesn't have cancer the probability that a woman will have a positive ultrasound result is 4%. Post-prob(Woman=40_BreastCancer+ IF Woman_Mammogram+) Prior-prob(Woman=40_BreastCancer+) x Pred-prob(Woman_Mammogram+ IF Woman=>40_BreastCancer+) [Prior-prob(Woman>40_BreastCancer+) x Pred-prob(Woman_Mammogram+ IF Woman>40_BreastCancer+)] + [Prior-prob(Woman240_BreastCancer-) x Pred-prob(Woman_Mammogram+ IF Woman240_BreastCancer-)] Post-prob(Woman>40_BreastCancer+ IF Woman_Ultrasound+) Prior-prob(Woman>40_BreastCancer+) x Pred-prob(Woman_Ultrasound+ IF Woman240_BreastCancer+) [Prior-prob(Woman>40_BreastCancer+) x Pred-prob(Woman_Ultrasound+ IF Woman>40_BreastCancer+)] + [Prior-prob(Woman>40_BreastCancer-) x Pred-prob(Woman_Ultrasound+ IF Woman>40_BreastCancer-)] According to the information given in the problem what is the prediction probability that a randomly selected woman over 40 years with breast cancer will test positive for breast cancer on a mammography test? 1% 80% 10% 95% 4% Question 11 1/1 pts https://canvas.ubc.ca/courses/132235/quizzes/708094 7/8
2/16/24, 9:06 PM E1 Practice 5 Medical tests and Bayes: PHIL 125 003 2023W2 Introduction to Scientific Reasoning Physicians often use two diagnostic tests to determine whether a woman has breast cancer. These are the mammography and the ultrasound test. The results of the two tests are independent of one another. f a woman has breast cancer a positive result on one test doesn't increase or decrease the chance of a positive result on the other test. If a woman doesn't have breast cancer the result on one test doesn't affect the chance of a postive or negative result on the other test. The incidence rate of breast cancer for women at age 40 or older is 1%. ff a woman in this age group has breast cancer the probability is 80% that she will have a positive mammography result. f she doesn't have breast cancer there is still a 10% chance that she will get a positive mammogram. ff a woman 40 or older has breast cancer the chance is 95% that she will have a positive ultrasound test result. On the other hand, if she doesn't have cancer the probability that a woman will have a positive ultrasound result is 4%. Post-prob(Woman=40_BreastCancer+ IF Woman_Mammogram+) Prior-prob(Woman=40_BreastCancer+) x Pred-prob(Woman_Mammogram+ IF Woman=>40_BreastCancer+) [Prior-prob(Woman>40_BreastCancer+) x Pred-prob(Woman_Mammogram+ IF Woman>40_BreastCancer+)] + [Prior-prob(Woman240_BreastCancer-) x Pred-prob(Woman_Mammogram+ IF Woman240_BreastCancer-)] Post-prob(Woman>40_BreastCancer+ IF Woman_Ultrasound+) Prior-prob(Woman>40_BreastCancer+) x Pred-prob(Woman_Ultrasound+ IF Woman240_BreastCancer+) [Prior-prob(Woman>40_BreastCancer+) x Pred-prob(Woman_Ultrasound+ IF Woman>40_BreastCancer+)] + [Prior-prob(Woman>40_BreastCancer-) x Pred-prob(Woman_Ultrasound+ IF Woman>40_BreastCancer-)] You have a woman patient over 40. Assume that there is nothing special about your patient. For example, she isn't known to have a family history of breast cancer. Suppose she tests negative on an ultrasound test. What is the resulting probability given this test result that she doesn't have breast cancer? (Answers have been rounded to 0 decimal places.) 100% 96% 99% 81% Quiz Score: 11 out of 11 https://canvas.ubc.ca/courses/132235/quizzes/708094 8/8