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

Review exercises 28 931
(d) A component is picked atrandom. What is the
probability itis notacceptable?
(e) A component is picked atrandom. Itisnot
acceptable. What isthe probability itwas made
by machine B?
(f) A component is picked atrandom and is
acceptable. What isthe probability itwas made
by eithermachine Aormachine B?
3 MachinesMandNmanufacture components. The
probability that acomponent isofan acceptable
standard is 0.93 when manufactured bymachine M
and0.86 when manufactured by machine N. Machine
Msupplies70% ofthe components andmachine N
suppliesthe rest.
(a) Calculate the probability that acomponent picked
atrandom is ofan acceptable standard.
(b) Acomponent isnot ofan acceptable standard.
Calculate the probability that itismade by
machine N.
(c) Two components are picked at random. Calculate
the probability that they are made bydifferent
machines.
4 E 1 is the event the component is reliable.E 2 is the
event the component ismade bymachine A. State
(a) E 1
(b) E 2
(c) E 1 ∩E 2
(d) E 1 ∪E 2
(e) E 2 ∩E 1
5 Thelifespans,L,of2500components were measured
andthe resultswere recorded in Table 28.6.
Table28.6
Lifespan(hours)
Numberofcomponents
0L<200 76
200 L<300 293
300 L<400 574
400 L<500 1211
500 L<600 346
(a) Calculate the probability thatacomponenthas a
lifespanofover 400 hours.
(b) Calculate the probability thatacomponenthas a
lifespanofless than300 hours.
(c) Calculate the probability thatacomponentthat
lasts for300 hours willcontinueto lastforat
least 500 hours.
6 Given the eventsE 1 ,E 2 andE 3 are
E 1 :the circuitisfunctioning
E 2 :the circuitismadeby machine A
E 3 :the circuitwilllast foratleast600 hours state
(a) E 2
(b) E 3
(c) E 1 ∪E 2
(d) E 1 ∩E 3
(e) E 2 ∩E 3
7 A data stream consistsofthe characters A, B,C,D
andE, with respective probabilities of0.16,0.23,
0.31, 0.12 and0.18.
(a) Calculate the informationassociated with the
character B.
(b) Calculate the entropy.
(c) Calculate the redundancy.
8 The probabilityacomponentis reliableis0.93.Three
components are picked atrandom. Calculatethe
probability that
(a) all components are unreliable
(b) exactly onecomponent isreliable
(c) at leastonecomponentis reliable
(d) exactly two components are reliable
9 A circuitis asshown in Figure 28.9.Thecircuitis
operational ifcurrent can flowfrom Pto Q alongany
route. Theprobability thatresistor typeAis faultyis
0.09, andforresistor typeBthe probability ofafault
is 0.14.Calculate the probability thatthe circuitis
operational.
P
Figure28.9
A
A
10 The probabilityacomponentis reliableis0.96.Five
components are picked atrandom. Calculatethe
probability that
(a) allfive components are reliable
(b) none are reliable
(c) atleast oneis reliable
B
A
B
Q