 
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 oddnumbered"
