Tap every statement that follows from independence

Exercise and reference answers

Questions

1. Items

   1. Text

      P(E ∩ F) = P(E) P(F)

      Matches the category

      Yes

   2. Text

      P(E|F) = P(E)

      Matches the category

      Yes

   3. Text

      P(F|E) = P(F)

      Matches the category

      Yes

   4. Text

      P(E ∩ F) = 0

      Matches the category

      No

   5. Text

      P(E) + P(F) = 1

      Matches the category

      No

   Category

   Follows from E and F being independent

2. Items

   1. Text

      The events partition the sample space

      Matches the category

      Yes

   2. Text

      They are pairwise disjoint

      Matches the category

      Yes

   3. Text

      Each has nonzero probability

      Matches the category

      Yes

   4. Text

      They are all equally likely

      Matches the category

      No

   5. Text

      They are independent of each other

      Matches the category

      No

   Category

   Needed for Bayes' theorem to apply

Explanation