5.X. Bayes’ Theorem – Complete Detail

Try these first

1. 1.

   What is the definition of sample space?

   Hint

   Think about all things that can happen in a probability experiment.

2. 2.

   Explain conditional probability using the notation P(A|B).

   Hint

   Focus on what is known when B happens.

3. 3.

   What is Bayes’ Theorem primarily used for?

   • To measure central tendency
   • To update probabilities based on evidence
   • To calculate variance

   Hint

   Think about how you adjust your beliefs when new information comes.

4. 4.

   True or False: The posterior probability is the same as the prior probability.

   • True
   • False

   Hint

   Recall the definitions of prior and posterior.

5. 5.

   A factory produces two types of items: A and B. Items A have a defect rate of 5%, while items B have a defect rate of 10%. If 70% of items produced are of type A, what is the probability that a randomly selected defective item came from type B?

   Hint

   Consider applying the theorem with both defect rates and prior production proportions.

6. 6.

   In a clinical trial, a med shows a 90% treatment response rate. However, 15% of non-responders still show improvement due to external factors. How is this scenario modeled using Bayes’ Theorem to assign probabilities upon observing a response?

   Hint

   Survey how patient responses lead to refined probabilities regarding treatment efficacy.