082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

930 Chapter 28 Probability
probabilitiesare 0.94, 0.91,0.97 and0.94,
respectively, formachines 1, 2, 3 and 4.
(a) Acapacitor istaken from each machine. What is
the probability all fourcapacitors are acceptable?
(b) Twocapacitorsaretakenfrommachine1andtwo
from machine 2. What isthe probability all four
capacitors are acceptable?
(c) Acapacitor istaken from each machine.
Calculate the probability that atleastthree
capacitors are acceptable.
(d) Acapacitor istaken from each machine. From
thissampleoffour capacitors, one istaken at
random.
(i) What is the probability itis acceptable and
made by machine 1?
(ii) What is the probability itis acceptable and
made by machine 2?
(e) Acapacitor istaken from each machine. From
thissampleoffour capacitors, one istaken at
random. What isthe probability itis acceptable?
[Hint: use the resultsin (d).]
Solutions
1 (a) 0.196 (b) 0.112 (c) 0.2401
2 (a) 0.0049 (b) 0.8649 (c) 0.0651
(d) 0.9951
3 (a) 0.7787 (b) 5.12 ×10 −4
(c) 0.2031 (d) 0.9818
4 (a) 0.2025 (b) 0.15 (c) 0.375
(d) 0.4375 (e) 0.355
5 (a) 0.7800 (b) 0.7317 (c) 0.9808
(d) (i) 0.235 (ii) 0.2275 (e) 0.94
REVIEWEXERCISES28
1 Componentsare made bymachines A, B and C.
Machine Amakes 30% ofthe components, machine
B makes50% ofthe components and machine C
makes the rest. Theprobability that a component is
acceptable when made by machine Ais 0.96, when
made bymachine Bthe probability is0.91 andwhen
made bymachine Cthe probability is0.93.
(a) Acomponent is picked atrandom. Calculate the
probability that itis made bymachine C.
(b) Acomponent is picked atrandom. Calculate the
probability that itis made byeither machine Aor
machine C.
(c) Acomponent is picked atrandom. Calculate the
probability that itis made bymachine Band is
acceptable.
(d) Acomponent is picked atrandom. Calculate the
probability that itis notacceptable.
(e) Acomponent picked atrandom is notacceptable.
Calculate the probability that itismade by
machine A.
(f) Acomponent picked atrandom is acceptable.
Calculate the probability that itismade by either
machine Aormachine B.
(g) Two components are picked atrandom. Calculate
the probability that they are both acceptable.
(h) Two components are picked atrandom. Calculate
the probability that oneis acceptable and oneis
unacceptable.
2 Three machines, A, Band C,manufacture a
component. Machine A manufactures 35%ofthe
components, machine B manufactures 40%ofthe
components and machine C makesthe rest.A
component is eitheracceptable ornotacceptable: 7%
ofcomponents made bymachine Aare not
acceptable, 12%ofcomponents made by machine B
are not acceptable and 2% ofthosemade bymachine
Care alsonotacceptable.
(a) Findthe probability that acomponent is made by
eithermachine Aormachine B.
(b) Two components are picked atrandom. What is
the probability that they are both made by
machine B?
(c) Three components are picked atrandom. What is
the probability they are each made by adifferent
machine?