standard_description: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.
problem_activity: Problem 1
Which tree diagram corresponds with which table? How do you know?
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Problem 2
In a certain population, 30% of people get a particular disease. A test was developed to determine if any given person has the disease, but it isn’t perfect.
The test has a 90% chance of accurately predicting that someone has a disease, BUT it also has a 5% chance of predicting someone has this disease who doesn’t.
Below are two models you can use to visualize this situation.
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Using the information from the problem, write in the number of people in a random sample of 2,000 who take the test for the disease and get results that are true positive, false positive, true negative, and false negative.


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