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SOLUTION
MANUAL
KEYING YE AND SHARON MYERS
for
ESSENTIALSOF
PROBABILITY&STATISTICS FORENGINEERS&SCIENTISTS
WALPOLE,MYERS,MYERS,YE 1 / 4
Chapter 1 Introduction to Statistics and Probability 1.1 (a)S={8,16,24,32,40,48}.(b) Forx 2 +4x−5=(x+ 5)(x−1) = 0, the only solutions arex=−5 andx=1.
S={−5,1}.
(c)S={T,HT,HHT,HHH }.(d)S={N. America,S. America,Europe,Asia,Africa,Australia,Antarctica}.(e) Solving 2x−4≥0 givesx≥2. Since we must also havex<1, it follows that S=φ.
1.2S={(x, y)|x 2 +y 2 <9;x≥0,y≥0}.
1.3 (a)A={1,3}.(b)B={1,2,3,4,5,6}.(c)C={x|x 2 −4x+3=0}={x|(x−1)(x−3) = 0}={1,3}.(d)D={0,1,2,3,4,5,6}. Clearly,A=C.
1.4S={A
1A2,A1A3,A1A4,A2A3,A2A4,A3A4}.
1.5S={1HH,1HT,1TH,1TT,2H,2T,3HH,3HT,3TH,3TT,4H,4T,5HH,5HT,5TH,
5TT,6H,6T}.
1.6 (a)A={1HH,1HT,1TH,1TT,2H,2T}.(b)B={1TT,3TT,5TT}.(c)A Γ
={3HH,3HT,3TH,3TT,4H,4T,5HH,5HT,5TH,5TT,6H,6T}.
(d)A Γ
∩B={3TT,5TT}.
(e)A∪B={1HH,1HT,1TH,1TT,2H,2T,3TT,5TT}.Copyrightc≤2013 Pearson Education, Inc..
1 2 / 4
2Chapter 1Introduction to Statistics and Probability 1.7 (a)S={M
1M2,M1F1,M1F2,M2M1,M2F1,M2F2,F1M1,F1M2,F1F2,F2M1,F2M2,
F 2F1}.(b)A={M
1M2,M1F1,M1F2,M2M1,M2F1,M2F2}.
(c)B={M
1F1,M1F2,M2F1,M2F2,F1M1,F1M2,F2M1,F2M2}.
(d)C={F
1F2,F2F1}.
(e)A∩B={M
1F1,M1F2,M2F1,M2F2}.
(f)A∪C={M
1M2,M1F1,M1F2,M2M1,M2F1,M2F2,F1F2,F2F1}.
(g) A
A B
B C S ∩ 1.8 (a)S={FFF,FFN,FNF,NFF,FNN,NFN,NNF,NNN }.(b)E={FFF,FFN,FNF,NFF }.(c) The second river was safe for fishing.
1.9 A Venn diagram is shown next.S P F Sample Space 1.10 (a)S={ZY F,ZNF,WY F,WNF,SY F,SNF,ZY M }.(b)A∪B={ZY F,ZNF,WY F,WNF,SY F,SNF }=A.(c)A∩B={WYF,SYF}.
1.11 (a)A∪C={0,2,3,4,5,6,8}.(b)A∩B=φ.CopyrightcΦ2013 Pearson Education, Inc. 3 / 4
Solutions for Exercises in Chapter 13 (c)C ffi
={0,1,6,7,8,9}.
(d)C ffi ∩D={1,6,7},so(C ffi
∩D)∪B={1,3,5,6,7,9}.
(e) (S∩C) ffi =C ffi
={0,1,6,7,8,9}.
(f)A∩C={2,4},soA∩C∩D ffi
={2,4}.
1.12 (a)M∪N={x|0 1.13 A Venn diagram is shown next. AB S 123 4 (a) From the above Venn diagram, (A∩B) ffi contains the regions of 1, 2 and 4.(b) (A∪B) ffi contains region 1.(c) A Venn diagram is shown next.A B C S 1 2 3 4 5 6 7 8 (A∩C)∪Bcontains the regions of 3, 4, 5, 7 and 8. 1.14 (a) Not mutually exclusive.(b) Mutually exclusive.(c) Not mutually exclusive.(d) Mutually exclusive. 1.15 (a) The family will experience mechanical problems but will receive no ticket for traffic violation and will not arrive at a campsite that has no vacancies.(b) The family will receive a traffic ticket and arrive at a campsite that has no va- cancies but will not experience mechanical problems.Copyrightc≤2013 Pearson Education, Inc.
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