Probability outcome

The uncertainty may be addressed by constructing a base case which represents the most probable outcome, and then performing sensitivities around this case to determine which of the inputs the project is most vulnerable to. The most influential parameters may then be studied more carefully. Typical sensitivities are considered in Section 13.7, Sensitivity Analysis . 

When averaged over the distribution of energy loss for a low-LET radiation (e.g., a 1-MeV electron), the most probable event in liquid water radiolysis generates one ionization, two ionizations, or one ionization and excitation, whereas in water vapor it would generate either one ionization or an excitation. In liquid water, the most probable outcomes for most probable spur energy (22 eV) are one ionization and either zero (6%) or one excitation (94%) for the mean energy loss (38 eV), the most probable outcomes are two ionizations and one excitation (78%), or one ionization and three excitations (19%). Thus, it is clear that a typical spur in water radiolysis contains only a few ionizations and/or excitations. 

Likewise, any system of interest can be in any one of a number of possible states and each state is represented by a column vector to produce a matrix X whose columns correspond to the possible states. The probable outcome of any measurement of the observable A on system X is described by the scalar products of all possible a x> representing individual probabilities. 

If there is no hypothesis for the event, use an inductive method to find potential scenarios. Inductive methods speculate a given fault or failure, then look forward in time to determine the probable outcome, that is, What would happen if... Inductive methods include using a Checklist or a Hazard and Operability Analysis (HAZOP). 

What are the potential consequences of this type of incident occurring at your facility What is the most probable outcome Why ... 

Consider a firm s decision about how much to invest in research and development. To decide rationally, the firm must estimate the probable outcome of the investment — how likely it is that its innovative activities will lead to a profitable innovation - as well as the investments made by other firms and the probable outcome of those investments. Now the outcome of innovative activities is inherently uncertain. The firm cannot foresee with any precision whether it will hit the jackpot or come out with empty hands. Against the background of a constantly changing technology, past records are not good predictors of future success. 

The FDA s decision to allow the investigation of a new drug to enter each of these next phases, and the decision of the sponsor on the value of pursuing the full course of investigations through to the NDA submission, are based largely on the statistician s estimations of the probable outcomes. 

When equilibrium constants are known they provide information about the probable outcome of a reaction (the extent to which products have been formed), but care must be taken when using them in discussion. 

A forecast as to the probable outcome of an attack or disease, the prospect as to recovery from a disease as indicated by the nature and symptoms of the case. 

What is a probable outcome of the thermal reprocessing of a recovered mixture of nylon resins Discuss options. 

As you might expect, the most probable outcome is 2 actives (probability 0.375) and the least probable outcomes are 0 and 4 actives (each with a probability of 0.0625). We can use the cumulative probability distribution to answer other probability questions of interest. For example, what is the probability of observing 3 or fewer actives This probability is denoted as P(A < 3) = 0.9375. We can use the complement rule from Section 6.2 to calculate the probability of observing 2 or more actives, P(X > 2), as ... 

It is possible to use the computational tools of quantitative thermodynamics to predict the course of an equilibrium process and to determine the most probable outcome or product formed. Unfortunately, classical thermodynamics does not address time-related questions that fall within the realm of... 

There has been much controversy about the proper definition of probability. One definition is the following If an experiment has n equally probable outcomes, m of which are favorable to the occurrence of a certain event A, then the probability that A occurs is m/n. Note that this definition is circular, since it specifies equally probable outcomes when probability is what we are attempting to define. It is simply assumed that we can recognize equally probable outcomes. An alternative definition is based on actually performing the experiment many times. Suppose that we perform the experiment N times and that in M of these trials the event A occurs. The probability of A occurring is then defined as... 

For example, suppose we ask for the probability of drawing a heart when a card is picked at random from a standard 52-card deck containing 13 hearts. There are 52 cards and hence 52 equally probable outcomes. There are 13 hearts and hence 13 favorable outcomes. Therefore m/n = 13/52 = 1/4. The probability for drawing a heart is 1/4. 

Another story is that the fourteenth-century German monk and alchemist Berthold Schwartz was the inventor of modern firearms. According to this version of events, it was in Freiburg, Germany, about a century after Roger Bacon s forays into the alchemy of explosives, that the black Monk Berthold married gunpowder with a workable firearm. Berthold s ultimate fate is uncertain. He may have either accidentally blown himself up—the most probable outcome, if he had in fact existed at all—or even been executed because of his infernal discoveries. In fact, very little documentation of his life exists at all ... 

Maximizing Multiplicity Predicts the Highest Probability Outcomes... 

Blaise Pascal (1623-1662) was a French mathematician and philosopher who became interested in probability when some gambler friends asked him how to predict the probable outcome of a game of chance that could not be finished. 

To identify the potential hazards in your chemical processes, a process hazard analysis (PHA) must be conducted. The facility should set up a team to conduct facility investigations and evaluations on processes that might be dangerous. This hazard analysis team should focus on the location of each process area, the hazards of the process, the probable outcome if controls fail, and the possibility of human error. The prudent facility manager makes a careful review of the plant s historical record concerning previous incidents—those that caused or could have caused catastrophic results. When the analysis is completed and recommendations have been issued to management for resolving the safety issues identified, this document becomes a permanent plant record that should be updated every five years. 

Write chemical equations to represent the most probable outcome in each of the following. If no reaction is likely to occur, so state. 

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