Assertion and reason: the multiplication rule

Exercise and reference answers

Questions

1. Reason

   You may condition on either event, provided its probability is nonzero.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   P(E ∩ F) can be written two different ways.

2. Reason

   Independence makes P(F|E) equal to P(F).

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   For independent events the multiplication rule simplifies.

3. Reason

   Bayes' theorem has a sum in its denominator.

   Verdict

   Both are true; the reason does not explain the assertion.

   Assertion

   Conditional probability lies between 0 and 1.

Explanation