Math Probability Day 5 Worksheet Key

Algebra 2 Honors Mutually Exclusive and Independent Events A single card is drawn from a standard deck of 52 cards. Find the probability of drawing the indicated card. Not an ace 48/52 = 12/13 A face card and a 4 0 No single card that is both. A heart or a diamond 13/52 + 13/52 = 1/2 A 6 or a 7 4/52 + 4/52 = 2/13 An ace or a spade 4/52 + 13/52 - 1/52 = 4/13 Only one card is both an ace and spade. An ace and a spade 1/52 Two six-sided dice are rolled. Find the probability of the given event. The sum is greater than 4 30/36 = 5/6 The sum is 6 or 11 5/36 + 2/36 = 7/36 The sum is neither 5 nor 9 1 - P(sum is 5 or 9) 1 - (4/36 + 4/36) = 7/9 The sum is greater than 7 and less than 11 12/36 = 1/3 The sum is even 36/36 = 1 The sum is 3 or 9 2/36 + 4/36 = 1/6 The sum is not 8 1 - P(sum is 8) 1 - 5/36 = 31/36 The sum is less than 10 and greater than 5 20/36 = 5/9 Tennis: You and your best friend are members of a high school tennis team. The coach is about to pick one player to be the captain of the team. You estimate that there is a 34% chance1 that you will be picked and a 54% chance that your best friend will be picked. What is the probability that either you or your best friend will be picked?2   16. Meteorology: Probability of rain today: 65% Probability of rain tomorrow: 25% Probability of rain both days: 35% What is the probability that it will rain today or tomorrow? P(today or tomorrow) = P(today) + P(tomorrow) - P(both) = 65/100 + 25/100 - 35/100 = 11/20 17. Parakeets: 18 light green parakeets (5 females, 13 males) 25 sky blue parakeets (15 females, 10 males) What is the probability that a randomly chosen parakeet is male or sky blue? P(male or sky blue) = P(male) + P(sky blue) - P(male and sky blue) = 23/43 + 25/43 - 10/43 = 38/43 18. Biology: 30 plants: 12 visible light, 15 UV light, 6 both What is the probability that a plant receives either visible or UV light? P(visible or UV) = P(visible) + P(UV) - P(both) = 12/30 + 15/30 - 6/30 = 7/10 19. Potluck Dinner: 3 people choose from 10 recipes. What is the probability at least 2 bring the same? P(2 or more) = 1 - P(None) = 1 - (10/10) * (9/10) * (8/10) = 7/25 20. Book Collection: 20 horror, 15 romance, 25 mystery novels. What is the probability that at least one of each type is picked in 4 books? P(at least one of each type) = (20C1 * 15C1 * 25C2 + 20C1 * 15C2 * 25C1 + 20C2 * 15C1 * 25C1) / 60C4 = 21380/487635 21. Home Electronics: 5 houses with 1000 possible garage door opener codes. What is the probability at least 2 have the same code? P(2 or more) = 1 - P(None) = 1 - (1000/1000) * (999/1000) * ... = 1 - (1000P5 / 1000^5) ≈ 0.009965 Find the probability of drawing the given cards from a standard deck of 52 cards. First, with replacement and then without.   A jack, then a diamond With replacement: 13/52 * 13/52 = 1/16 Without replacement: 13/52 * 13/51 = 13/204 A 5, then a face card, then an ace With replacement: 4/52 * 12/52 * 4/52 = 3/2197 Without replacement: 4/52 * 12/51 * 4/50 = 8/825 A king, then another king, then a third king With replacement: 4/52 * 4/52 * 4/52 = 1/2197 Without replacement: 4/52 * 3/51 * 2/50 = 1/5525 An ace, then a face With replacement: 4/52 * 12/52 = 3/169 Without replacement: 4/52 * 12/51 = 4/221 A two, then a joker With replacement: 4/52 * 0/52 = 0 Without replacement: 4/52 * 0/51 = 0 Marbles: A jar contains 12 red marbles, 16 blue marbles, and 18 white marbles. Three marbles are chosen without replacement. What is the probability none of them are white? 28/46 * 27/45 * 26/44 = 273/1265 Four marbles are chosen without replacement. What is the probability that they are all white? 18/46 * 17/45 * 16/44 * 15/43 = 204/10879 Three marbles are chosen without replacement. What is the probability that at least one is white? P(1 or more) = 1 - P(None) = 1 - 28/46 * 27/45 * 26/44 = 992/1265 Apples: Probability of selecting a good apple from a basket: 86% Find the probability of selecting 3 good apples when selecting 1 apple from each of 3 different baskets. P(3 good) = 0.86 * 0.86 * 0.86 = 0.636056 Tea: 2 lemon, 3 orange-mango, 3 chamomile, 1 apricot-ginger Kevin chooses two at random. What is the probability that he chose a lemon, then a chamomile? P(lemon, then chamomile) = (2/9) * (3/8) = 1/12 What is the probability that he grabbed 2 orange-mango and a lemon all at once? P(2 orange-mango, 1 lemon) = (3C2 * 2C1) / 9C3 = 3*2 / 84 = 1/14 Money: 5 quarters, 2 dimes, 3 nickels Three coins are removed at the same time What is the probability that you grab 2 nickels and a quarter? P(2 nickels, 1 quarter) = (3C2 * 5C1) / 10C3 = 15/120 = 1/8 What is the probability that you have 40¢ in your hand? P(40¢) = (5C1 * 2C1 * 3C1) / 10C3 = 30/120 = 1/4 What is the probability that you have 10¢ in your hand? P(10¢) = (5C2 * 2C1) / 10C3 = 10/120 = 1/6 Color Spinner: If you spin the arrow twice, what is the probability that the arrow will land on a white wedge, then a red? P(white, then red) = (3/12) * (4/12) = 1/12 If you spin the arrow three times, what is the probability that the arrow will land on a red, blue, and then blue wedge again?1   P(red, blue, blue) = (4/12) * (3/12) * (3/12) = 1/48