Assertion and reason

Exercise and reference answers

Questions

1. Reason

   P(F) sits in the denominator of the definition.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   P(E|F) requires P(F) ≠ 0.

2. Reason

   The denominator sums over every branch, so the branches must cover S once.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   Bayes' theorem needs the events to form a partition.

3. Reason

   Mutually exclusive events satisfy P(E ∩ F) = 0.

   Verdict

   The assertion is false and the reason is true.

   Assertion

   Two mutually exclusive events with nonzero probability are independent.

4. Reason

   Conditioning on F still leaves a complete probability model.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   P(E′|F) = 1 − P(E|F).

Explanation