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Conditional Independence 1

)Suppose that we have a box that contains two coins:

1. A fair coin:P(H)=P(T)=0.5
2. A two-headed coin:P(H)=1

A coin is chosen at random from the box, i.e. either coin is chosen with probability1/2

, and tossed twice. Conditioned on the identity of the coin, the two tosses are independent.

Define the following events:

• EventA: first coin toss isH
• EventB: second coin toss isH

• EventC: two coin tosses result inHH
• EventD: the fair coin is chosen.

For the following statements, decide whether they are true or false.

1. AandBare independent.