Chapter 12 Study Guide of Geometry

Chapter 12 Study Guide Geometry Sample Spaces and Probability What is the probability that the sum of the numbers on a number cube is a multiple of 3? 36/170 What is the probability that the sum of the numbers on a number cube is a multiple of 2? 50% On a game at an amusement park, 45 customers bought coffee or orange juice. 32 customers bought coffee, and 25 customers bought orange juice. How many customers bought both coffee and orange juice? 12 customers A medical study found that 62.2% of the people in the United States have type O blood. The study also found that 8.5% of the U.S. population has type AB blood. Suppose a person is randomly selected from the U.S. population. Assume that blood type is independent of gender. Do not round intermediate computations. 0.622 x 0.085 = 0.05287 Independent and Dependent Events A die is rolled and a coin is tossed. Two people are randomly chosen from a group of 10 men and 8 women. Are these events independent or dependent? Independent The spinner is spun and a die is rolled. Independent Find the probability of selecting 7 red marbles from a bag containing 5 red marbles and 5 blue marbles, without replacement. 0 Find the probability of selecting 7 red marbles from a bag containing 5 red marbles and 5 blue marbles, with replacement. 0.00390625 Tree Diagrams, Tables, and Probability Create a tree diagram to show the possible outcomes. Create a table to show the possible outcomes. A restaurant offers 3 different types of pizza crusts, 4 different meats, and 3 different vegetables. How many different pizzas are possible? 36 different pizzas What is the probability that a randomly selected customer will order a pizza with a thin crust, pepperoni, and mushrooms? 1/36 What is the probability that a randomly selected customer will order a pizza with a thin crust and pepperoni? 1/12 What is the probability that a randomly selected customer will order a pizza with mushrooms? 1/3 Determine whether ordering "thin crust" and "being older than 18" are independent events. Not Independent Chapter 12 Study Guide Geometry 12.1 Sample Spaces and Probability Find the probability of each event when two six-sided dice are rolled. a) The sum is greater than 8. [P(x>8)=\frac{10}{36}=\frac{5}{18}=0.278] b) The sum is not 3. [P(x\neq3)=\frac{35}{36}=0.972] You throw a dart at the board shown. Your dart is equally likely to hit any point inside the square board. What is the probability that your dart lands in one of the two yellow sections in the smaller circle?   Geo Probability = Area Want / Total Area Fraction and Decimal 25.1% 12.2 Independent and Dependent Events Nine women and six men are on a committee. Two people are randomly chosen from the committee members to serve as a chairperson and a treasurer. Find the probability that both events A and B will occur.   A: The chairperson is a man. B: The treasurer is a woman. [P(chair:man) \cdot P(treasurer:woman) = \frac{6}{15} \cdot \frac{9}{14} = \frac{3}{5} \cdot \frac{9}{14} = \frac{27}{70} = 38.6%] A: The chairperson is a woman. B: The treasurer is a woman. [P(chair:woman) \cdot P(treasurer:woman) = \frac{9}{15} \cdot \frac{8}{14} = \frac{3}{5} \cdot \frac{4}{7} = \frac{12}{35} = 34.3%] Find the probability of randomly selecting 3 of the given marbles from a bag containing 10 red marbles and 5 blue marbles when a) you replace each marble before selecting the next, and b) you do not replace each marble before selecting the next one. Which probability is most likely to occur?   all three are red, independently [\frac{5}{15} \cdot \frac{5}{15} \cdot \frac{5}{15} = \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} = \frac{1}{27} = 3.7%] [\frac{5}{15} \cdot \frac{4}{14} \cdot \frac{3}{13} = \frac{1}{3} \cdot \frac{2}{7} \cdot \frac{3}{13} = \frac{2}{91} = 2.2%] [\frac{5}{15} \cdot \frac{10}{15} \cdot \frac{10}{15} = \frac{1}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} = \frac{4}{27} = 14.8%] [\frac{5}{15} \cdot \frac{10}{14} \cdot \frac{9}{13} = \frac{1}{3} \cdot \frac{5}{7} \cdot \frac{3}{13} = \frac{15}{91} = 16.5%]