Suppose that S = {a,b,c,d,e}, all outcomes equally likely, and E = {a,b}. List all the events in this space that are independent of E ? Urn A contains 3 red balls and 1 green ball, and urn B contains no red balls and 75 green balls. The action will be: select one of urns A, B, or C at random (meaning they are equally likely to be selected), and draw one ball from it. How many balls of each color should be in urn C, if the event "a green ball is selected" is to be independent of "urn C is chosen," and urn C is to contain as few balls as possible? 6. Is it possible for two events to be both independent and mutually exclusive? If so, in what circumstances does this happen?