**Quote:**

P(E AND F) = 0 if E and F are independent.

Not true, P(E AND F) = 0 if E and F are MUTUALLY EXCLUSIVE.

To say that E and F are independent means only that the outcome of E has no effect on the outcome of F and vice versa.

**Quote:**

P(E OR F) = P(E) + P(F) - P(E AND F) is true if E and F are dependent events.However if they are independent Events P(E OR F) = P(E) + P(F)

If they are independent events you still need the -P(E and F)

For example:

If you flip two coins (coins 1 and 2) at the same time, and we call the event that coin 1 lands heads "E" and the event the coin 2 lands heads "F", what is P(E or F)?

P(E) = .5

P(F) = .5

P(E or F) does not equal 1.