Suppose you rolls fair die.....

Suppose you roll a fair die. Let A be the event that you roll at most a 4. Let B be the event that you roll an even number. 11. (1 pt) List all the outcomes in each of the three following sets: (i) the sample space; (ii) event A; and (iii) event B. What is the experiment being performed? 12. (2 pts) For each of parts (a) through (h), do the following two things: (1) draw the Venn Diagram; and (2) INTERPRET using the language of probability. (a) AUB (e) A'UB (b) AnB (f) AUB' (c) A - B (9) (AU B)' (d) B - A (h) (An B)' 13. (1 pt) Find each of the eight probabilities P(A U B), P(An B), P(A - B), P(B - A), P(A' U B), P(A U B'), P((A U B)'), and P((An B)'). Remember, the die is fair. Suppose now that the die is loaded, i.e. unfair. Consider the same events A and B from the previous three problems. 14. (1 pt) If P(A) = 0.50 and P(B) = 0.35, what is the largest possible value of P(AUB)? The smallest possible value? 15. (1 pt EC) If P(A) = 0.45 and P(B) = 0.80, what is the largest possible value of P(An B)? The smallest possible value? [Note: this problem is not asking about A U B, but about An B.]