True or false: independence versus exclusivity

Exercise and reference answers

Questions

1. Statement is true

   No

   Statement

   Independent and mutually exclusive mean the same thing.

2. Statement is true

   Yes

   Statement

   For independent events, P(E ∩ F) = P(E) P(F).

3. Statement is true

   Yes

   Statement

   For mutually exclusive events, P(E ∩ F) = 0.

4. Statement is true

   Yes

   Statement

   Knowing F occurred leaves P(E) unchanged when E and F are independent.

5. Statement is true

   No

   Statement

   Mutually exclusive events with nonzero probabilities are independent.

Explanation