1 The probability a component is acceptable is 0.8. Four components are sampled. What is the probability that (a) exactly one is acceptable (b) exactly two are acceptable?
1 The probability a component is acceptable is 0.8. Four components are sampled. What is the probability that (a) exactly one is acceptable (b) exactly two are acceptable?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:EXERCISES 29.10
1 The probability a component is acceptable is 0.8. Four
components are sampled. What is the probability that
(a) What is the probability the machine is
acceptable?
(a) exactly one is acceptable
(b) What is the probability that six of the seven chips
are operating correctly?
(b) exactly two are acceptable?
2 A machine requires all seven of its micro-chips to
operate correctly in order to be acceptable. The
probability a micro-chip is operating correctly is 0.99.
(c) The machine is redesigned so that the original
seven chips are replaced by four new chips. The
probability a new chip operates correctly is 0.98.
the most likely number of valves to remain reliable
for more than 10 years?
Is the new design more or less reliable than the
original?
3 The probability a machine has a lifespan
5 years is 0.8. Ten machines are chosen at random.
What is the probability that
The probability a chip is manufactured to an
acceptable standard is 0.87. A sample of six chips is
picked at random from a large batch.
more than
(a) eight machines have a lifespan of more than 5
years
(a) Calculate the probability all six chips are
ассеptable.
(b) Calculate the probability none of the chips is
ассеptable.
(b) all machines have a lifespan of more than 5 years
(c) at least eight machines have a lifespan of more
than 5 years
(c) Calculate the probability that fewer than five
chips in the sample are acceptable.
(d) no more than two machines have a lifespan of
less than 5 years?
(d) Calculate the most likely number of acceptable
chips in the sample.
4 The probability a valve remains reliable for more than
10 years is 0.75. Eight valves are sampled. What is
(e) Calculate the probability that more than two
chips are unacceptable.
Solutions
1 (a) 0.0256 (b) 0.1536
4
6.
2 (a) 0.9321 (b) 0.0659 (c) 0.9224.
New design is less reliable
5 (a) 0.4336 (b) 4.826 x 10-6 (c) 0.1776 (d) 6
(e) 0.0324
3 (a) 0.3020 (b) 0.1074 (c) 0.678 (d) 0.678
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