Chapter 12 Exam Name: Answer the questions in the spaces provided. If you run out of room, show your work on a separate paper clearly numbered and attached to this exam. SHOW ALL YOUR WORK!!! Remember to answer the question in the proper format. 1. Match the word with the definition (1 point each - no partial credit!) Definitions Words i. An is a controlled operation that yields a set of results. a. empirical ii. The possible results of an experiment is called its. b. mutually exclusive iii. An is a subset of the outcomes of an experiment. c. equally likely outcomes iv. is determined through a study of the possible outcomes d. conditional that can occur for a given experiment. v. is determined from the actual observations = actual data of an experiment. e. independent events vi. If each outcome of an experiment has the same chance of f. event occurring as any other outcome, they are said to be. vii. A list of all possible outcomes of an experiment is called a g. tree diagrams. viii. Illustrated flow-charts used to determine sample spaces are h. permutation called. ix. Two events, A and B are if it impossible for both events i. outcomes to occur simultaneously. x. Events A and B are if the occurrence of either one, in j. combination no way affects the of the other one occurring. xi. The of event E 2 occurring, given that event E 1 has happened (or will happen; the time relationship does not k. theoretical matter), P (E 2 E 1 ), is called a. xii. A is any ordered arrangement of a given set of objects. l. sample space xiii. A is a distinct group (or subset) of objects, without m. experiment regard to their order.
2. (5 points each) (a) If P (A) = 0.3, P (B) = 0.9, and P (A and B) = 0.25, find P (A or B). P (A or B) = (b) If P (A) = 0.45, P (A and B) = 0.2, and P (A or B) = 0.3, find P (B). P (B) = 3. A red and a green die are tossed. Find the of each of the following: (a) P (the sum of the two numbers is odd) (b) P (the sum of the two numbers is 6) (c) P (the sum of the two numbers is less than 6 if the red die was a 2) 4. One card was drawn at random from a standard deck of 52 cards. Find the of each of the following: (2 points each) (a) P (the card is a jack) (b) P (the card is not a jack) (c) P (the card is black or an ace) (d) P (the card is a black ace) Page 2
5. A fair coin is tossed three times. A typical outcome, HHT, means that the first two tosses were heads and the last was a tail. (2 points each) (a) List the sample space: S = { (b) Find P (coin landing on no heads) (c) Find P (coin landing on at least one head) (d) Find P (coin landing on exactly two tails the first toss was a tail) 6. Calculate the following: (1 point each) (a) 5 P 3 (b) 7 P 5 (c) 5 C 3 (d) 7 C 5 7. (5 points each) (a) From a group of 12 students, nine are to be selected to be on the volleyball team. In how many ways can the team be selected? (b) From a group of 10 students, three are to selected to be officers, i.e. president, treasurer and secretary in a drama club. In how many ways can these officers be selected? Page 3
8. A sandwich at Quickie Lunch has wheat (W), french (F) or rye bread (R), cheddar (C) or Swiss cheese (S), and turkey (T) or ham (H). Assume that all sandwiches consist of one type of bread, one type of cheese, and one of the meats. (a) Make a tree diagram of all possible sandwiches that can be made with these ingredients. (b) How many different sandwiches are possible? (c) A typical outcome is WSH for a wheat sandwich with Swiss cheese and ham. List the sample space of all possible outcomes (=sandwiches). S = { 9. How many different arrangements (= dummy words ) are possible with the letters in MISSISSIPPI? (6 points) Page 4
10. A license plate consists of 2 letters followed by 3 digits. Determine the number of different license plates possible if: (3 points each) (a) Repetition of letters and digits is permitted. (b) Repetition of letters and digits is not permitted. (c) The first letter has to be an A and the first digit has to be a 5. 11. Two marbles are drawn from a box containing 3 red, 4 white, and 2 green marbles. (2 points each) (a) Find P (both marbles are white), if the marbles were drawn one at a time with (b) Find P (both marbles are white), if the marbles were drawn one at a time without (c) Find P (1st marble is white and 2nd one is green), if the marbles were drawn one at a time without (d) Find P (at least one marble is white), if the marbles were drawn one at a time without Page 5