5.X.4. Interpretation of Terms

Try these first

1. 1.

   What does prior probability refer to in Bayes' Theorem?

   Hint

   Think about what you know before an event occurs.

2. 2.

   Define likelihood in the context of Bayes' Theorem.

   Hint

   It's about determining evidence related to a belief.

3. 3.

   What does prior probability represent in Bayes’ Theorem?

   • Updated belief
   • Initial belief
   • Likelihood of evidence

   Hint

   Remember, it’s about what we know before seeing new evidence.

4. 4.

   True or False: Posterior probability is the same as prior probability.

   • True
   • False

   Hint

   Think about what happens after you see new evidence.

5. 5.

   A disease is known to affect 3% of the population. A new test has a 97% sensitivity (true positive) and a 4% false positive rate. Calculate the posterior probability of having the disease given a positive test result.

   Hint

   Remember to consider both true positives and false positives in your calculations.

6. 6.

   In a game show, a contestant initially selects one door out of three, then the host opens another door, revealing no prize behind it. If the contestant switches doors after the host reveals a door, what's the likelihood of winning the prize compared to sticking with the first choice?

   Hint

   Think about how the prior and posterior probabilities change with available evidence.