MATH 106 Week 5 LEO Discussion Topic Exercises Revised: 25 March 2016 PROBABILITY (Applied Finite Mathematics, \"Probability\") 1. A card is selected from a deck. Find the following probabilities. a. P (a red card) b. P (a face card) c. P (a jack and a spade) 2. A jar contains 6 red, 7 white, and 7 blue marbles. If a marble is chosen at random, find the following probabilities. a. b. c. d. P (red) P (white) P (red or blue) P (red and blue) 3. Consider a family of three children. Find the following probabilities. a. b. c. d. P (two boys and a girl) P (at least one boy) P (children of both sexes) P (at most one girl) 4. Two dice are rolled. Find the following probabilities. a. b. c. d. P (the sum of the dice is 5) P (the sum of the dice is 8) P (the sum is 3 or 6) P (the sum is more than 10) 5. A jar contains four marbles numbered 1, 2, 3, and 4. If two marbles are drawn, find the following probabilities. a. b. c. d. P (the sum of the number is 5) P (the sum of the numbers is odd) P (the sum of the numbers is 9) P (one of the numbers is 3) 1 MATH 106 Week 5 LEO Discussion Topic Exercises Revised: 25 March 2016 MUTUALLY EXCLUSIVE EVENTS AND THE ADDITION RULE Determine whether the following pair of events are mutually exclusive. 6. a. A = {A person earns more than $25,000} B = {A person earns less than $20,000} b. A card is drawn from a deck: C = {It is a King} D = {It is a heart} c. A single, fair, 6-sided die is rolled: E = {An even number shows} F = {A number greater than 3 shows} 7. a. Two fair 6-sided dice are rolled: G = {The sum of dice is 8} H = {One die shows a 6} b. Three fair coins are tossed: I = {Two heads come up} J = {At least one tail comes up} c. A family has three children: K = {First born is a boy} L = {The family has children of both sexes} Use the addition rule to find the following probabilities. 8. A card is drawn from a 52-card deck, and the events C and D are as follows: C = {It is a king} D = {It is a heart}. Find \"the probability of event C OR event D occurring\