which one hopes to avoid. Let P(B) = 0.001 while P(A) = 0.990. (a) Give P(C). (b) What is the probability that the machine does not underfill? %3D %3D (c) What is the probability that the machine either overfills or uderfills?

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It is common in many industrial areas to use
a filling machine to fill boxes full of product. This
occurs in the food industry as well as other areas in
which the product is used in the home, for example,
detergent. These machines are not perfect, and indeed
they may A, fill to specification, B, underfill, and C,
overfill. Generally, the practice of underfilling is that
which one hopes to avoid. Let P(B) = 0.001 while
P(A) = 0.990.
(a) Give P(C).
(b) What is the probability that the machine does not
underfill?
(c) What is the probability that the machine either
overfills or underfills?
Transcribed Image Text:It is common in many industrial areas to use a filling machine to fill boxes full of product. This occurs in the food industry as well as other areas in which the product is used in the home, for example, detergent. These machines are not perfect, and indeed they may A, fill to specification, B, underfill, and C, overfill. Generally, the practice of underfilling is that which one hopes to avoid. Let P(B) = 0.001 while P(A) = 0.990. (a) Give P(C). (b) What is the probability that the machine does not underfill? (c) What is the probability that the machine either overfills or underfills?
Factory workers are constantly encouraged to
practice zero tolerance when it comes to accidents in
factories. Accidents can occur because the working en-
vironment or conditions themselves are unsafe. On the
other hand, accidents can occur due to carelessness
or so-called human error. In addition, the worker's
shift, 7:00 A.M.-3:00 P.M. (day shift), 3:00 P.M.-11:00
P.M. (evening shift), or 11:00 P.M.-7:00 A.M. (graveyard
shift), may be a factor. During the last year, 300 acci-
dents have occurred. The percentages of the accidents
for the condition combinations are as follows:
Unsafe
Human
Shift
Conditions
Error
5%
6%
2%
If an accident report is selected randomly from the 300
Day
Evening
Graveyard
32%
25%
30%
reports,
(a) what is the probability that the accident occurred
on the graveyard shift?
(b) what is the probability that the accident occurred
due to human error?
(c) what is the probability that the accident occurred
due to unsafe conditions?
(d) what is the probability that the accident occurred
on either the evening or the graveyard shift?
Transcribed Image Text:Factory workers are constantly encouraged to practice zero tolerance when it comes to accidents in factories. Accidents can occur because the working en- vironment or conditions themselves are unsafe. On the other hand, accidents can occur due to carelessness or so-called human error. In addition, the worker's shift, 7:00 A.M.-3:00 P.M. (day shift), 3:00 P.M.-11:00 P.M. (evening shift), or 11:00 P.M.-7:00 A.M. (graveyard shift), may be a factor. During the last year, 300 acci- dents have occurred. The percentages of the accidents for the condition combinations are as follows: Unsafe Human Shift Conditions Error 5% 6% 2% If an accident report is selected randomly from the 300 Day Evening Graveyard 32% 25% 30% reports, (a) what is the probability that the accident occurred on the graveyard shift? (b) what is the probability that the accident occurred due to human error? (c) what is the probability that the accident occurred due to unsafe conditions? (d) what is the probability that the accident occurred on either the evening or the graveyard shift?
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