Suppose R is an equivalence relation on a set A and suppose a; b 2 A. Prove: a 2 b () b 2 a.

Math 2300 chapter 5 part I Find the indicated probability. 1) If two balanced die are rolled, the possible outcomes can be represented as follows. (1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2) (1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3) (1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4) (1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5) (1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6) Determine the probability that the sum of the dice is 6 or 12. 2) A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five people, list the possible samples of size three and use your list to determine the probability that B is included in the sample. (Hint: There are 10 possible samples.) Estimate the probability of the event. 3) In a certain class of students, there are12 boys from Wilmette, 3 girls from Kenilworth, 10 girls from Wilmette, 4 boys from Glencoe, 2 boys from Kenilworth and 5 girls from Glencoe. If the teacher calls upon a student to answer a question, what is the probability that the student will be from Kenilworth 4) A frequency distribution on employment information from Alpha Corporation follows.. Find the probability that an employee has been with the company