GSE Honors Geometry. 1. Create a lattice diagram representing the possible outcomes for the two tiles

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1 GSE Honors Geometry Unit 9 Applications of Probability Name Unit Test Review Part 1 You and a friend have made up a game that involves drawing one numbered tile out of each of two separate bags. The first bag contains tiles numbered 1-5, and the second bag contains tiles numbered Create a lattice diagram representing the possible outcomes for the two tiles 2. Identify the subset that contains all elements in which the sum of the two tiles is a multiple of three 3. What is the probability that the sum of the two tiles will be 8? 4. Find Psum is odd first tile is even 5. Find the probability that at least one of the two tiles shows an even number 6. Create a Venn Diagram to represent the possible outcomes of the two tiles. Circle A should represent the 1 st tile being an even number, and circle B should represent the 2 nd tile being an even number. 7. Find A B 8. Find A B 9. Find A B 10. Find B A 11. Find AB A A B 12. Find PA B 13. Find P A Part 2 As part of the current Statistics unit in your math class, your teacher has compiled data on which types of social media his students use. There are 26 students in the class, and each student is anonymously identified with a letter of the alphabet. The results of the poll are as follows: Facebook (FB): B, D, H, I, K, L, O, P, T, V, W, X, Z Twitter (TW): C, D, G, H, I, J, K, P, Q, R, S, U, X, Z Instagram (IN): B, E, H, J, K, L, Q, S, T, U, V, X, Y None: A, F, M, N 1. Draw a Venn Diagram to organize your outcomes

2 2. Find PFB 3. Find PTW IN 4. Find PTW 5. Find PIN FB 6. Find PFB TW IN 7. Find PIN FB TW Part 3 You are writing an article for the school newspaper about local sports teams. As part of the article you decide to take a poll in order to try and see which team, the Braves or the Falcons, have more fans in the junior and senior classes. The results of your poll are recorded in the following table: Braves Falcons Juniors Seniors Draw a Venn Diagram to organize your outcomes 2. Use the table to evaluate each of the following probabilities: a. PB b. PF c. P J d. PS e. PB S f. PB S g. PF S h. P F S i. PF J j. PF S k. Find the probability that a given junior prefers the Falcons, and represent it using proper notation

3 l. Given that the student is a senior, find the probability that he/she prefers the Braves, and represent it using proper notation m. Find the probability that a given junior does not prefer the Falcons, and represent it using proper notation n. Find the probability that a student prefers the Falcons, given that he/she is a senior o. Show that the conditional probability formula works for PB S Part 4 Find the missing probability 1. For two events S and Q it is known that PQ 0.72 and PS Q 0.48 Find PS Q 2. For two events X and Y it is known that P X and PX Y Find PY X For two events B and C it is known that PC B 0.78 and PC B 0.25 Find PB 4. For two events V and W it is known that PW and Find PV W P V W. 15 Part 5 A local BBQ restaurant is known for having not only the best sweet tea in town, but also the best lemonade. For marketing purposes, the lunchtime manager of the restaurant is trying to determine whether or not either drink is more likely to accompany a certain choice of meat. She decides to conduct a random survey of her customers, and the results are shown in the table below: Bubba s BBQ Chicken Pork Beef Sweet Tea Lemonade

4 1. Find the following probabilities (write as percentages): a. PB b. PL c. PS P d. PL C 2. For each of the six possible meat/drink combinations, determine whether that pair seems to represent a dependent or an independent relationship. Part 6 The following data is for a group of 850 people: 67 of them are known to have lung cancer 94 of them have smoked cigarettes at some point in their lives 63 of the 67 that have lung cancer have smoked cigarettes 1. Organize the data using the table below: has lung cancer smoked cigarettes did not smoke cigarettes does not have lung cancer smoked cigarettes did not smoke cigarettes 2. Find the following probabilities: a. P(a person smoked cigarettes given that he/she has lung cancer) b. P(a person smoked cigarettes given that he/she does not have lung cancer) c. P(a person has lung cancer given that he/she smoked cigarettes) d. P(a person has lung cancer given that he/she has not smoked cigarettes) e. P(a person does not have lung cancer given that he/she smoked cigarettes) f. P(a person does not have lung cancer given that he/she did not smoke cigarettes)

5 3. Determine whether or not the events of having lung cancer and smoking cigarettes are independent. Show all relevant calculations. 4. Determine whether or not the events of not having lung cancer and not smoking cigarettes are independent. Show all relevant calculations. Part 7 In the spinner to the right, the regions have a 1:2 ratio. 1. P($600) = 2. P($300) = 3. P(at least $700) = 4. P(less than $400) = 5. P(at most $600) = Calculate the following probabilities given two spins. 6. P(sum of $300) = 7. P(sum of at most $400) = 8. P(sum of at least $1500) = 9. P(sum of at least $500) = 10. P(sum of $200 first spin lands on $100) = 11. P(sum of at least $1000 first spin lands on $800) = Part 8 A card is chosen at random from a standard deck of 52 playing cards. 1. Find the probability that the card is an eight or an ace. 2. Find the probability that the card is an eight or a heart. 3. Find the probability that the card is the nine of hearts or any diamond. 4. Find the probability that the card is red or an even card. You draw a card from a bag that contains 6 white cards numbered 1-6 and 6 gold cards numbered 1-6. Tell whether the events A and B are mutually exclusive or overlapping. Then find P(A or B). 5. Event A: you choose a white card Event B: you choose a gold card 6. Event A: you choose a #2 card Event B: you choose a gold card 7. Event A: you choose a white card Event B: you choose a #6 card 8. Event A: you choose a #5 card Event B: you choose an even-numbered card

6 Part 9 There are 27 marbles in a bag. 10 are blue, nine are red, and eight are green. If a blue marble is drawn from the bag and not replaced, calculate the probability of each of the following occurring on the 2 nd draw. 1. P(green) = 2. P(red or blue) = 3. P(not green) = There are 24 marbles in a bag. Eight are blue, eight are white, and eight are gold. If the marbles are not replaced after the 1 st draw, what is the probability of each of the following occurring in the given order? 4. P(white, blue)= 5. P( white, blue, gold) = 6. P(white or blue, gold) = 7. P(gold first draw was a white marble) = Using a standard deck of 52 cards, 3 cards are dealt without replacement. 8. What is the probability that all three cards are even? 9. What is the probability of being dealt three face cards? 10. If the first card is a diamond, what is the probability that the second card will not be a diamond? 11. What is the probability of being dealt 3 cards from the odd cards? Part 10 Vocabulary Mutually exclusive Independent Probability (and its range) Percentage (and its range) Overlapping or Inclusive Dependent Conditional Probability Complement