Consider tossing two fair coins and the events A: Head in the first toss B: Head in

Question:

Consider tossing two fair coins and the events A: Head in the first toss B: Head in the second toss C: Both heads or both tails in the two tosses
(a) Verify that the property of independence holds for all event pairs.
(b) Show that P(ABC) is different from the product P(A) P(B) P(C). (This illustrates the fact that pair wise independence does not ensure complete independence.)