True or false: total probability and Bayes

Exercise and reference answers

Questions

1. Statement is true

   Yes

   Statement

   The denominator of Bayes' theorem is the total probability of A.

2. Statement is true

   Yes

   Statement

   Total probability needs the events to partition the sample space.

3. Statement is true

   No

   Statement

   Bayes' theorem gives P(A|Eᵢ) from P(Eᵢ|A).

4. Statement is true

   Yes

   Statement

   Bayes' theorem gives P(Eᵢ|A) from P(A|Eᵢ).

5. Statement is true

   No

   Statement

   A partition may include an event of zero probability.

Explanation