Consider a standard 6-sided die and a biased die with sides (1,2,3,4,6,6), i.e. one which has no 5 and two 6's. Assume you pick one of the two dice, with equal probability, and roll it twice. Define the events A1 = 1st roll is 6 and A2 = 2nd roll is 6. Show that the two events are conditionally independent given the chosen die (either standard or biased).