HW1_11_soln - IE 111 Fall 2011 Homework #1 Solutiions...

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IE 111 Fall 2011 Homework #1 Solutiions Question 1 Three events are shown on the Venn diagram in the following figure: Produce the figure and shade the region that corresponds to each of the following events. a) B b) A B
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c) (A B) C d) (A C)
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e) (A B) C Question 2 Consider the Venn diagram at right with events A, B, C, and D as shown
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a) Give a set representation of the shaded region. A C D or A C D ′∩ B Indicate the most appropriate answer for each of the following questions (where NMI means “need more information”). b) T F NMI (A B ) D and (A D) C are mutually exclusive. F c) T F NMI P(B) ≤ P(D) NMI Using the Venn diagrams to verify the following set theory d) (A B) =A ′∩ B
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Question 3 A digital scale is used that provides weights to the nearest gram. a) What is the sample space for this experiment? Answer: Integers from 0 to infinity (since no upper weight limit was given for the scale) Let A denote the event that a weight exceeds 11 grams, let B denote the event that a weight is less than or equal to 15 grams, and let C denote the event that a weight is greater than or equal to 8 grams and less than 12 grams. Describe the following events. b) A B c)A B d)A e) A B C f) (A C) g) A B C h) B ′∩ C i) A B C a) Answer: S= nonnegative integers from 0 to the largest integer that can be displayed by the scale S={0,1,2,3,…} b) S c) {12, 13, 14, 15} d) {0,1, 2,…,11} e) S f){0,1,2,….7} g) Ǿ h)Ǿ i) {8,9,10,…} Question 4 An experiment consists of flipping a coin and then tossing a die once if the coin shows head. If the coin shows tail, the die is tossed twice. a) Describe the sample space by listing its elements. b) Describe the sample space using a tree diagram. Answer: a) S= {(H1), (H2), (H3), (H4), (H5), (H6), (T11), (T12), (T13), (T14), (T15), (T16), (T21), (T22), (T23), (T24), (T25), (T26), (T31), (T32), (T33), (T34), (T35), (T36), (T41), (T42), (T43), (T44), (T45), (T46), (T51) , (T52), (T53), (T54), (T55), (T56), (T61), (T62), (T63), (T64), (T65), (T66)} b)
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Question 5 For the sample in question 4: a) List the element of event A: a number less than 3 occurs on a die b) List the element of event B: a tail occurs c) List the elements of event A
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This note was uploaded on 10/13/2011 for the course IE 111 taught by Professor Storer during the Fall '07 term at Lehigh University .

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HW1_11_soln - IE 111 Fall 2011 Homework #1 Solutiions...

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