True or false: conditional probability

Exercise and reference answers

Questions

1. Statement is true

   Yes

   Statement

   P(E|F) = P(E ∩ F) ÷ P(F), provided P(F) ≠ 0.

2. Statement is true

   No

   Statement

   P(E|F) can be greater than 1.

3. Statement is true

   Yes

   Statement

   P(E′|F) = 1 − P(E|F).

4. Statement is true

   No

   Statement

   P(E|F) is defined even when P(F) = 0.

5. Statement is true

   Yes

   Statement

   0 ≤ P(E|F) ≤ 1 always holds.

Explanation