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

28.4 Complementary events 913
EXERCISES28.3
1 Acomponent is classifiedasone oftopquality,
standard quality orsubstandard, with respective
probabilities of0.07,0.85 and 0.08.Findthe
probability that acomponent is
(a) either topquality orstandard quality
(b) not topquality
2 Thelifespan (L)ofeach of2000 valvesis measured
andgiven in Table 28.3.
Table28.3
Thelifespans of2000valves.
Lifespan(hours)
Number
L 1000 119
800 L<1000 520
600 L<800 931
400 L<600 230
L < 400 200
Calculate the probability that the lifespanofavalve is
(a) more than800 hours
(b) less than600 hours
(c) between 400 and 800 hours
3 Chipsare manufactured bymachines A andB.
Machine Amakes65% ofthe chips and machine B
makesthe remainder. Theprobability that a chipis
faulty is0.03 when made bymachine A and 0.05
when made by machine B.Achip isselected at
random. Calculate the probability that itis
(a) faulty andmade by machine A
(b) faulty ormade bymachine A
(c) faulty ormade bymachine B
(d) faulty andmade by machine B
(e) faulty
4 Componentsare made bymachines A, B,Cand D.
Machine A makes25%ofthe components, machine
B makes16% ofthe components, machine Cmakes
21% ofthe components and machine Dmakes the
remainder. The probability that acomponent is
acceptable is0.92 when made bymachine A, 0.90
when made by machine B,0.96 when made by
machine Cand 0.93 when made by machine D. A
component ispicked at random. Calculate the
probability that itis
(a) made by machine Aormachine C
(b) made by machines A, B orD
(c) acceptable andmade by machine B
(d) acceptable andmade by machine C
(e) acceptable andmade by machine B oracceptable
and made bymachine C
(f) acceptable ormade bymachine A
(g) acceptable
Solutions
1 (a) 0.92 (b) 0.93
2 (a) 0.3195 (b) 0.215 (c) 0.5805
3 (a) 0.0195 (b) 0.6675 (c) 0.3695
(d) 0.0175 (e) 0.037
4 (a) 0.46 (b) 0.79 (c) 0.144
(d) 0.2016 (e) 0.3456 (f) 0.949
(g) 0.929
28.4 COMPLEMENTARYEVENTS
Consider an electronic circuit. Clearly, either the circuit works correctly or it does not
workcorrectly.LetAbetheeventthatthecircuitworkscorrectly,andletBbetheevent
that the circuit does not work correctly. EitherAorBmust happen when the circuit is
tested, and one excludes the other. The eventsAandBare said to be complementary.