ECO 329 Slesnick Problem Set 1 1. Suppose that one card is to be selected from a deck of 20 cards that contains 10 red cards numbered 1 through 10 and 10 blue cards numbered 1 through 10. Let the event A be the event that a card with an even number is selected, let B be the event that a blue card is selected, and let C be the event that a card with a number less than 5 is selected. Describe the sample space S and describe each of the following events in words: (a) AnBAC (b) Bn C (c) AUBUC (d) An (B UC) (e) Acn Bon Co 2. Verify, using a Venn diagram, which of the following relationships are true or false: (a )(A U B) - C = AU (B - C) (b) AUB = (A - (An B) ) UB (c) (A U B) - A = B (d) (A n B' n C) is contained in (A U B) (e) (A U B ) n C = (At n C) U (B* n C) 3. If the probability that student A will fail a certain statistics exam is 0.5, the probability that student B will fail the exam is 0.2, and the probability that both student A and student B will fail is 0.1, what is the probability that at least one of these two students will fail the exam? 4. Consider two events A and B with P(A) = 0.4 and the P(B) = 0.7. Determine the maximum and minimum possible values for P(An B) and the conditions under which these values are obtained. 5. Two fair dice are rolled simultaneously. Let A denote the event "the sum shown is 8" and Let B denote the event "the two dice show the same number". Find P(A), P(B), P( An B), P(A/B) and P(B/A). 6. If four dice are rolled, what is the probability that each of the four numbers that appear will be different