Table 2. Problem formulations for both contexts (breast cancer screening problem and HIV testing problem).

	Breast cancer screening problem		HIV testing problem
	Probability version	Natural frequency version	Probability version	Natural frequency version
Medical situation	Imagine that you are a physician in a mammography screening center where women without symptoms are screened for breast cancer. In addition to mammograms, you frequently use sonograms as a supplementary medical test to detect breast cancer. At the moment, you are advising a woman who has no symptoms but who has received a positive result from her mammogram as well as a positive result from her sonogram. This woman wants to know what these results mean for her. For your answer, there is the following information available, which is based on a random sample of women who have all undergone a mammography and a sonography1:		Imagine that you are a physician in an AIDS information center. In addition to individual counseling interviews, your information center also provides HIV testing, for which two blood samples are taken: An ELISA test is conducted with the first blood sample. If the ELISA test is positive (indicating a possible HIV infection), a Western Blot test is ordered with the second blood sample. At the moment, you are advising a low-risk client who has received a positive result from the ELISA test as well as from the Western Blot test. This client wants to know what these results mean for him. For your answer, there is the following information available, which is based on a random sample of low-risk persons who have all undergone both the ELISA and the Western Blot test1:
Presen-tation of informa-tion	• Text only • Tree only • Text and tree	• Text only • Tree only • Text and tree	• Text only • Tree only • Text and tree	• Text only • Tree only • Text and tree
Text	The probability of breast cancer for a woman with no symptoms is 1%. The probability that a woman with breast cancer will have a positive mammogram is 80%. The probability that a woman with breast cancer will have a positive sonogram is 95%. The probability that a woman without breast cancer will have a false-positive mammogram is 9.6%. The probability that a woman without breast cancer will have a false-positive sonogram is 7.8%. 1 Footnote: Assume for your calculations that the results of both tests are (statistically) independent for women with breast cancer as well as for women without breast cancer.	100 out of 10,000 women with no symptoms will have breast cancer. 80 out of 100 women with breast cancer will have a positive mammogram. 76 out of 80 women with breast cancer and a positive mammogram will have a positive sonogram. 950 out of 9,900 women without breast cancer will have a false-positive mammogram. 74 out of 950 women without breast cancer but with a positive mammogram will have a false-positive sonogram. 1 Footnote: Assume for your calculations that the results of both tests are (statistically) independent for women with breast cancer as well as for women without breast cancer.	The probability of an HIV infection for a low-risk client is 0.01%. The probability that an HIV-infected client will have a positive ELISA test result is 99.9%. The probability that an HIV-infected client will have a positive Western Blot test result is 99.8%. The probability that a client without HIV infection will have a false-positive ELISA test result is 0.4%. The probability that a client without HIV infection will have a false-positive Western Blot test result is 0.1%. 1 Footnote: Assume for your calculations that the results of both tests are (statistically) independent for HIV-infected clients as well as for clients who are not HIV-infected.	100 out of 1,000,000 low-risk clients are HIV-infected. 100 out of 100 HIV-infected clients will have a positive ELISA test result. 100 out of 100 HIV-infected clients with a positive ELISA test result will have a positive Western Blot test result. 4,000 out of 999,900 clients without an HIV infection will have a false-positive ELISA test result. 4 out of 4,000 clients without an HIV infection but with a positive ELISA test result will have a false-positive Western Blot test result. 1 Footnote: Assume for your calculations that the results of both tests are (statistically) independent for HIV-infected clients as well as for clients who are not HIV-infected.
Tree diagram	Probability tree (in the tree-only and in the text-and-tree version)	Natural frequency tree (in the tree-only and in the text-and-tree version)	Probability tree (in the tree-only and in the text-and-tree version)	Natural frequency tree (in the tree-only and in the text-and-tree version)
Question	What is the probability that a woman with both positive mammogram and positive sonogram actually has breast cancer?	How many of the women with both positive mammogram and positive sonogram actually have breast cancer?	What is the probability that a client with both positive ELISA test and positive Western Blot test results is actually HIV-infected?	How many of the clients with both positive ELISA test and positive Western Blot test results are actually HIV-infected?
	Answer: _______	Answer: ____ out of ____	Answer: _______	Answer: ____ out of ____