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

924 Chapter 28 Probability
3 years 5 years
100
92 (reliable)
83 (reliable)
}
9 (unreliable)
17 (unreliable)
8 (unreliable) 8 (unreliable)
Figure28.8
Tree diagram forEngineering application 28.13.
EXERCISES28.6
1 Acomponent is manufactured bymachines 1 and2.
Machine 1 manufactures 72% oftotal production of
the component. Thepercentage ofcomponents which
are acceptable varies, depending uponwhich machine
is used.Formachine 1, 97% ofcomponents are
acceptable and formachine 2, 92% are acceptable. A
component ispicked at random.
(a) What is the probability itwasmanufactured by
machine 1?
(b) What is the probability itisnot acceptable?
(c) What is the probability that itis acceptable and
made bymachine 2?
(d) If the component isacceptable what is the
probability itwasmanufactured bymachine 2?
(e) If the component isnot acceptable what isthe
probability itwasmanufactured bymachine 1?
2 Themeasured lifespans (L)of1500components are
recorded in Table 28.4.
Table28.4
Lifespansof1500components.
Lifespan(hours)
Numberofcomponents
L 1000 210
900 L<1000 820
800 L<900 240
700 L<800 200
L<700 30
(a) Whatistheprobabilitythatacomponentwhichis
still workingafter800 hours willlast foratleast
900 hours?
(b) Whatistheprobabilitythatacomponentwhichis
still workingafter900 hours willcontinue to last
foratleast 1000 hours?
3 Thelifespan,L,of1000 components is measuredand
detailed in Table 28.5.
Table28.5
Lifespansof1000 components.
Lifespan(hours)
Numberofcomponents
L 1750 70
1500 L<1750 110
1250 L<1500 150
1000 L<1250 200
750 L<1000 317
500L<750 96
250L<500 42
L<250 15
(a) Calculate the probability that the lifespanofa
component is more than 1000hours.
(b) Calculate the probability that the lifespanofa
component is lessthan 750 hours.
(c) Calculate the probability that a component which
isstill workingafter 500 hours willcontinue to
last forat least1500hours.
4 MachinesA, Band C manufacture components.
Machine Amakes 50%ofthe components, machine
Bmakes 30%ofthe components andmachine C
makesthe rest. Theprobability that acomponent is
reliable is0.93 when made bymachine A, 0.90 when
made bymachine Band 0.95 when made by machine
C.Acomponent is picked atrandom.
(a) Calculate the probability that itis reliable.
(b) Calculate the probability that itis made by
machine B given itisunreliable.