A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Concept explainers

Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axi…
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between…
Question
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?
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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?
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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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