MIDTERM EXAMINATION I, MATH 5651 (SPRING 2007) Notation: I use the notation AB = AB below in order to keep formulas from Summary: MIDTERM EXAMINATION I, MATH 5651 (SPRING 2007) ANSWER KEY Notation: I use the notation AB = AB below in order to keep formulas from getting too long and ugly. You may also use such notation. Problem 1 (15 points) Suppose that one card is selected at random from a deck of 16 cards consisting of 8 red cards numbered from 1 to 8 and 8 green cards numbered from 1 to 8. Let A be the event that a card with an odd number is selected; let B be the event that a red card is selected; and let C be the event that a card with a number greater than 3 is selected. (i) Describe the sample space S for the experiment. Then describe each of the following sets as subsets of S: (ii) ABC (iii) A(BC) (iv) BCc (v) Ac Bc Cc (vi) A B C Solution (i) The sample space can be described as S = {R1, R2, R3, R4, R5, R6, R7, R8, G1, G2, G3, G4, G5, G6, G7, G8}. Here R stands for red and G stands for green. For example, we have A = "selected card is odd-numbered" Collections: Mathematics