a) An inspector of the Alaska Pipeline has the task of comparing the reliability of two pumping stations. Each station is susceptible to two kinds of failure: pump failure and leakage. When either (or both) occur, the station must be shut down. The data at hand indicate that the following probabilities prevail: Station P(Pump Failure) P(Leakage) P(Both) 1 0.07 0.10 0 2 0.09 0.12 0.06 Which station has the lower probability of being shut down? What type of probability estimates are these (classical, relative, or subjective)?
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 axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
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 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
a) An inspector of the Alaska Pipeline has the task of comparing the reliability of two pumping stations. Each station is susceptible to two kinds of failure: pump failure and leakage. When either (or both) occur, the station must be shut down. The data at hand indicate that the following probabilities prevail:
|
Station |
P(Pump Failure) |
P(Leakage) |
P(Both) |
|
1 |
0.07 |
0.10 |
0 |
|
2 |
0.09 |
0.12 |
0.06 |
Which station has the lower
What type of probability estimates are these (classical, relative, or subjective)?
(b) From the following Venn diagram, which indicates the number of outcomes of an experiment corresponding to each
What type of probability estimates are these (classical, relative, or subjective)?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 6 images
