5.X.5. Example Problem

Try these first

1. 1.

   What does the term 'prior probability' refer to?

   Hint

   Think about what you believe before you get new data.

2. 2.

   In the example problem, what is the false positive rate?

   Hint

   It's the rate at which those without the disease test positive.

3. 3.

   What is Bayes' Theorem primarily used for?

   • Calculating averages
   • Updating probabilities
   • Finding probabilities of independent events

   Hint

   Recall the purpose of the theorem.

4. 4.

   True or False: The false positive rate represents the probability of testing negative when the disease is present.

   • True
   • False

   Hint

   Understand what false positive means.

5. 5.

   A screening test for a particular cancer is 90% sensitive (true positive rate) and 85% specific (true negative rate). If the prevalence of the cancer in the population is 0.05, calculate the probability that a person has cancer given a positive test result.

   Hint

   Break down the known probabilities and apply Bayes' formula.

6. 6.

   A new survey finds that 2% of a population has a particular disease. If a diagnostic test identifies it with a true positive rate of 88% and a false positive rate of 7%, determine the probability that someone has the disease after testing positive.

   Hint

   Use the known rates for true and false conditions to compute the posterior probability.