Suppose that we have a box that contains two coins: A fair coin: P(H)=P(T)=0.5 . A two-headed coin: P(H)=1 . A coin is chosen at random from the box, i. e. either coin is chosen with probability 1/2 , and tossed twice. Conditioned on the identity of the coin, the two tosses are independent. Define the following events: Event A : first coin toss is H . Event B : second coin toss is H . Event C : two coin tosses result in HH . Event D : the fair coin is chosen. For the following statements, decide whether they are true or false. A and B are independent.