Three of these are wrong. Find the one that holds.

Exercise and reference answers

Questions

1. Question

   Three of these statements about P(E|F) are false.

   Choices

   1. Item

      It equals P(E ∩ F) ÷ P(F)

      Correct

      Yes

   2. Explanation

      That is P(F|E), the other way round.

      Item

      It equals P(F ∩ E) ÷ P(E)

   3. Explanation

      It needs P(F) ≠ 0.

      Item

      It is defined for any F

   4. Explanation

      Every probability lies in [0, 1].

      Item

      It can exceed 1

2. Question

   Three of these statements about independence are false.

   Choices

   1. Item

      P(E ∩ F) = P(E) P(F)

      Correct

      Yes

   2. Explanation

      That is mutual exclusivity, not independence.

      Item

      P(E ∩ F) = 0

   3. Explanation

      The product rule is for intersection.

      Item

      P(E ∪ F) = P(E) P(F)

   4. Explanation

      That describes mutually exclusive events.

      Item

      Independent events cannot both occur

Explanation