Suppose that a fair coin is independently tossed two times L

Suppose that a fair coin is independently tossed two times. Let

A: Head appears on the first toss

B: Head appears on the second toss

C: Both tosses yield the same outcome

State whether each of the statements are True or False. Justify your answers with valid arguments

(a) All pairs (A, B), (A,C), and (B,C) are independent events.

(b) P(ABC) = P(A)P(B)P(C)

1. false. all events are not independent since the C statement depends on the occurence of A&B

2. False. this relation holds only for events that are independent