Table 2.
Item difficulties for individual items—Study 1
| Item | Item difficulty |
|---|---|
| Q11. Which of the following numbers represents the biggest risk of getting a disease? (1 in 12 or 1 in 37) | 96.1 |
| Q5. Which of the following numbers represents the biggest risk of getting a disease? (1%, 10%, or 5%) | 94.5 |
| Q4. Which of the following numbers represents the biggest risk of getting a disease? (1 in 100, 1 in 1000, or 1 in 10) | 92.7 |
| Q8a. If the chance of getting a disease is 10%, how many people would be expected to get the disease? Out of 100? | 91.2 |
| Q8b. Out of 1000? | 88.1 |
| Q9. If the chance of getting a disease is 20 out of 100, this would be the same as having a _____% chance of getting the disease. | 84.3 |
| Q1. Imagine that we roll a fair, six‐sided die 1000 times. Out of 1000 rolls, how many times do you think the die would come up as an even number? | 74.9 |
| Q13. Imagine that you are taking a class and your chances of being asked a question in class are 1% during the first week of class and double each week thereafter (i.e., you would have a 2% chance in Week 2, a 4% chance in Week 3, an 8% chance in Week 4). What is the probability that you will be asked a question in class during Week 7? | 74.3 |
| Q6. If Person A's risk of getting a disease is 1% in 10 years, and Person B's risk is double that of A's, what is B's risk? | 71.2 |
| Q2. In the BIG BUCKS LOTTERY, the chances of winning a $10.00 prize are 1%. What is your best guess about how many people would win a $10.00 prize if 1000 people each buy a single ticket from BIG BUCKS? | 70.6 |
| Q10. The chance of getting a viral infection is .0005. Out of 10 000 people, about how many of them are expected to get infected? | 58.4 |
| Q7. If Person A's chance of getting a disease is 1 in 100 in 10 years, and person B's risk is double that of A, what is B's risk? | 55.3 |
| Q14. Suppose that 1 out of every 10 000 doctors in a certain region is infected with the SARS virus; in the same region, 20 out of every 100 people in a particular at‐risk population also are infected with the virus. A test for the virus gives a positive result in 99% of those who are infected and in 1% of those who are not infected. A randomly selected doctor and a randomly selected person in the at‐risk population in this region both test positive for the disease. Who is more likely to actually have the disease? | 52.8 |
| Q3. In the ACME PUBLISHING SWEEPSTAKES, the chance of winning a car is 1 in 1000. What percent of tickets of ACME PUBLISHING SWEEPSTAKES win a car? | 34.5 |
| Q16 (CRT). If it takes five machines 5 minutes to make five widgets, how long would it take 100 machines to make 100 widgets? | 32.3 |
| Q17 (CRT). In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake? | 31.9 |
| Q15 (CRT). A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost? | 18.7 |
| Q12. Suppose you have a close friend who has a lump in her breast and must have a mammography … The table below summarizes all of this information. Imagine that your friend tests positive (as if she had a tumor), what is the likelihood that she actually has a tumor? | 9.8 |