TABLE 5.

Problem formulations.

	Mammography problem		Economics problem
	Probability version	Natural frequency version	Probability version	Natural frequency version
Cover story	Imagine you are a reporter for a women’s magazine and you want to write an article about breast cancer. As a part of your research, you focus on mammography as an indicator of breast cancer. You are especially interested in the question of what it means when a woman has a positive result (which indicates breast cancer) in such a medical test. A physician explains the situation with the following information:		Imagine you are interested in the question, of whether career-oriented students are more likely to attend an economics course. Therefore the school psychological service evaluates the correlations between personality characteristics and choice of courses for you. The following information is available:
Visualization	• Text only (no visualization): The probability of breast cancer is 2% for a woman who participates in routine screening. If a woman who participates in routine screening has breast cancer, the probability is 80% that she will have a positive test result. If a woman who participates in routine screening does not have breast cancer, the probability is 10% that she will have a positive test result.	• Text only (no visualization): 200 out of 10,000 women who participate in routine screening have breast cancer. Out of 200 women who participate in routine screening and have breast cancer, 160 will have a positive result. Out of 9,800 women who participate in routine screening and have no breast cancer, 980 will also have a positive result.	• Text only (no visualization): The probability that a student attends the economics course is 32%. If a student attends the economics course, the probability that he is career-oriented is 64%. If a student does not attend the economics course, the probability that he is still career-oriented is 60%.	• Text only (no visualization): 320 out of 1,000 students attend the economics course. Out of 320 students who attend the economics course, 205 are career-oriented. Out of 680 students who not attend the economics course, 408 are still career-oriented.
	• 2 × 2 table (prob.), or • double-tree (prob.), or • net diagram (prob.)	• 2 × 2 table (nat. freq.), or • double-tree (nat. freq.), or • net diagram (nat. freq.)	• 2 × 2 table (prob.), or • double-tree (prob.), or • net diagram (prob.)	• 2 × 2 table (nat. freq.), or • double-tree (nat. freq.), or • net diagram (nat. freq.)
Question 1 – cond. prob.	What is the probability that a woman who participates in routine screening and receives a positive test result has breast cancer?	How many of the women who participate in routine screening and receive a positive test result have breast cancer?	What is the probability that a student attends the economics course if he is career-oriented?	How many of the students who are career-oriented attend the economics course?
	Answer: ____ out of ____	Answer: _______	Answer: ___ out of ____	Answer: _______
Question 2 – joint prob.	What is the probability that a woman who participates in routine screening receives a negative test result and has breast cancer?	How many of the women who participate in routine screening receive a negative test result and have breast cancer?	What is the probability that a student attends the economics course and is not career-oriented?	How many of the students are not career-oriented and attend the economics course?
	Answer: _______	Answer: ____ out of ____	Answer: _______	Answer: ____ out of ____