Two are true, one is not

Exercise and reference answers

Questions

1. False statement

   P(E|F) may exceed 1

   Statements

   1. P(E|F) needs P(F) ≠ 0
   2. P(E′|F) = 1 − P(E|F)
   3. P(E|F) may exceed 1

2. False statement

   Bayes' theorem requires all branches to be equally likely

   Statements

   1. Bayes' theorem requires all branches to be equally likely
   2. Bayes' theorem needs a partition of the sample space
   3. Total probability sums P(Eᵢ)P(A|Eᵢ) over the partition

3. False statement

   Mutually exclusive always implies independent

   Statements

   1. Independent events satisfy P(E ∩ F) = P(E)P(F)
   2. Mutually exclusive always implies independent
   3. Mutually exclusive events satisfy P(E ∩ F) = 0

Explanation