Problem 3 [10 pts]: Independence i. We roll 2 twenty-sided dice, one at a time. Let A be the event the rst die rolls an odd number. Let B be the event the sum of both dice is an even number. Are A and B independent? Explain your reasoning. ii. A family has three children. Assume that having a child born that is left-hand dominant or right-hand dominant is equally likely. Let A be the event that the family has children that are lefthand and right-hand dominant, and B be the event that the family has at most 1 left-hand dominant child. Are the events A and B independent? Explain your reasoning