Page 84 - Applied statistics and probability for engineers

62 Chapter 2/Probability

in 1% of the messages, and a decode error occurs in 0.1% of the 2-218. Continuing Exercise 2-217, washers are selected from
messages. Assume the errors are independent. the lot at random without replacement.
(a) What is the probability of a completely defect-free message? (a) What is the minimum number of washers that need to be
(b) What is the probability of a message that has either an selected so that the probability that all the washers are
encode or a decode error? thinner than the target is less than 0.10?
2-213. It is known that two defective copies of a commer- (b) What is the minimum number of washers that need to be
cial software program were erroneously sent to a shipping lot selected so that the probability that 1 or more washers are
that now has a total of 75 copies of the program. A sample of thicker than the target is at least 0.90?
copies will be selected from the lot without replacement. 2-219. The following table lists the history of 940 orders
(a) If three copies of the software are inspected, determine the for features in an entry-level computer product.
probability that exactly one of the defective copies will be
found. Extra Memory
(b) If three copies of the software are inspected, determine the No Yes
probability that both defective copies will be found.
(c) If 73 copies are inspected, determine the probability that Optional high- No 514 68
both copies will be found. (Hint: Work with the copies that speed processor Yes 112 246
remain in the lot.)
Let A be the event that an order requests the optional high-
2-214. A robotic insertion tool contains 10 primary com- speed processor, and let B be the event that an order requests
ponents. The probability that any component fails during the extra memory. Determine the following probabilities:
(
(
warranty period is 0.01. Assume that the components fail inde- (a) P A∪ B) (b) P A∩ B)
(
pendently and that the tool fails if any component fails. What (c) P A′ ( B) (d) P A′ ∩ B′)
is the probability that the tool fails during the warranty period?
2-215. An e-mail message can travel through one of two (e) What is the probability that an order requests an optional
server routes. The probability of transmission error in each high-speed processor given that the order requests extra
of the servers and the proportion of messages that travel each memory?
route are shown in the following table. Assume that the servers (f) What is the probability that an order requests extra
are independent. memory given that the order requests an optional high-
speed processor?
Probability of Error
2-220. The alignment between the magnetic media and
Percentage head in a magnetic storage system affects the system’s perfor-
of Messages Server 1 Server 2 Server 3 Server 4 mance. Suppose that 10% of the read operations are degraded
Route 1 30 0.01 0.015 — — by skewed alignments, 5% of the read operations are degraded
Route 2 70 — — 0.02 0.003 by off-center alignments, and the remaining read operations are
(a) What is the probability that a message will arrive without properly aligned. The probability of a read error is 0.01 from
error? a skewed alignment, 0.02 from an off-center alignment, and
(b) If a message arrives in error, what is the probability it was 0.001 from a proper alignment.
sent through route 1? (a) What is the probability of a read error?
(b) If a read error occurs, what is the probability that it is due
2-216. A machine tool is idle 15% of the time. You request
to a skewed alignment?
immediate use of the tool on ive different occasions during the
year. Assume that your requests represent independent events. 2-221. The following circuit operates if and only if there is
(a) What is the probability that the tool is idle at the time of all a path of functional devices from left to right. Assume that
of your requests? devices fail independently and that the probability of failure of
(b) What is the probability that the machine is idle at the time each device is as shown. What is the probability that the circuit
of exactly four of your requests? does not operate?
(c) What is the probability that the tool is idle at the time of at
least three of your requests? 0.02
2-217. A lot of 50 spacing washers contains 30 washers that
are thicker than the target dimension. Suppose that 3 washers are
selected at random, without replacement, from the lot. 0.01 0.01
(a) What is the probability that all 3 washers are thicker than
the target?
(b) What is the probability that the third washer selected is 0.01 0.01
thicker than the target if the irst 2 washers selected are
thinner than the target?
(c) What is the probability that the third washer selected is 0.02
thicker than the target?