A probability model is a mathematical representation of a random phenomenon occurring. Probability is the study of long term behavior of random events in which outcomes cannot be predicted. During the experiment in the long run, patterns of outcomes emerge. A probability model includes its sample space, events that occur in the sample space, and possibilities associated with each event. When two events are independent there is no correlation of one event occurring for another event to occur. The first event does not influence the outcome of the second. This can be seen in the example of flipping a coin. When a coin is flipped and lands on heads three times determining which outcome will occur on the fourth flip would be an assumption. Just because the coin landed three times on heads does not mean that the fourth coin flip will land on heads. Actually, the chances of either event, (heads or tails), occurring is 50% or 0.5 or ½.
In the sample space of tossing two fair dice there we gather 36 different permutations. In sample space we can identify distinct events within the 36 permutations. One distinct event is having an outcome of two fair dices that have an outcome in which two dices sum are factors of 4. The outcomes that have factors of 4 are, (A, C), (B, B), (C, A), (D, D), (F, B), (B, F), (E, C), and (C, E). There are 8 summed permutations that equal 4. In the event of two fair dice being thrown would be an 8/36 chance, which is simplified as 2/9, which is 22% chance of receiving an outcome with the factor of 4. A second event is receiving an outcome of both dice receiving an outcome of both dices landing on a number less than 3. In the outcomes of this distinct event we have (A, A1), (A, B), (B, A), and (B, B1). We have a total of four outcomes in this distinct event. There is a 4/36, which is simplified as 1/9, or 11% chance of receiving an outcome where both independent dice are less than 3. Both
Probability is important for a stage in the study of treatments for many dread diseases. If a drug is being researched in its developmental stage, researchers calculate the maximum tolerated dose, whereas the dose has more toxic effects rather than health benefits.
Bayes Theorem, allows you to combine two or more probabilities into a single number. To come up with a combined probability, multiply the initial probability by a single number which represents the “likelihood ratio”. That ratio will either inflate or deflate the original probability estimate. The Bayes Theorem allows you to update your predictions over time as new and ideally better information comes to
There are 36 outcomes (elements) of rolling two dice, out of that 4 of them for getting 9 with the sum of even and odd numbers.
Mathematical models and computer simulations generate the most unqualified enthusiasm among campaigners. One of their underlying principles is that the biological effects of a chemical will depend on the size, shape, and other characteristics of its molecules, making it possible to predict toxicity without actual testing. The database on which such systems rely will, of course, have come from animal experiments. But once the relation between molecular structure and activity is understood, the toxicity of any new substance can be predicted with a computer instead of measured in a mouse.
Many theories of logic use mathematical terms to show how premises lead to conclusions. The Bayesian confirmation theory relates directly to probability. When applying this theory, a logician must know the probability of a given situation, have a conditional rule, and then he or she must apply the probability when the conditional rule is applied. This theory is used to determine an outcome based on a given condition. The probability of a given situation is x, when y occurs, or the probability is z if it does not occur. If y occurs, then the outcome of the given would be x. For example, if there is a high probability that a storm will occur if a given temperature drops and there is no temperature change, then it will most likely not rain because the temperature did not change (Strevens, 2012). By using observational data such as weather patterns, a person can arrive at a logical prediction or conclusion that will most likely come true based...
...ing. Moreover, if a treatment has the possibility of curing a child, but is unproven, even parents (who are eager to prolong the life of their children but lack the technical expertise to properly assess the risks involved) are not permitted to consent to it. Furthermore, Munson proposes that the IRB should be required to include outside experts to assess risks and benefits of experimental treatments.15
Introduction to the basic concepts of probability and statistics with discussion of applications to computer science.
The theory of determinism simply stated is the notion that all current events and everything we experience is determined by past occurrences and we have no control or freedom of choosing what happens in the future(McLeod). It is argued that determinism states that the future can predict and everything that has already happened in the past has an explanation to it. The predictability of events, however, is the principle and we can’t actually predict everything. It follows natural science laws to determine how predictable an occurrence is. If occurrence A is often followed by occurrence B, then A follows B, therefore if A occurs, the probability of B occurring can then be predictable. Several laws and statistical factors are ignored
The National Research Council in the United States has expressed its vision of “a not-so-distant future in which virtually all routine toxicity testing would be conducted in human cells or cell lines”, and science leaders around the world have reaffirmed this view. The sequencing of the human genome and birth of functional genomics, the explosive growth of computer power and computational biology, and high-speed robot automation of cell-based screening systems, to name a few, has sparked a quiet revolution in biology. Together, these innovations have produced new tools and ways of thinking that can help uncover exactly how chemicals and drugs disrupt normal processes in the human body at the level of cells and molecules. From there, scientists can use computers to interpret and integrate this information with data from human and population level studies. The resulting predictions regarding human safety and risk are potentially more relevant to people in the real world than animal tests. The wider field of human health research could benefit from a similar shift in theory. Many disease areas have seen little or no progress despite decades of animal research. Some 300 million people currently suffer from asthma, yet only two types of
In light of the findings of the study, the pharmacokinetic parameters of this drug would v...
Alternative methods are sometimes more reliable, more accurate, cost-effective, practical, and expedient Alternative testing can be used for in preclinical studies .These methods are vitro methods (human cells and tissues), silico models (advanced computer-modeling techniques), studies with human volunteers (microdosing, advanced brain imaging and recording techniques), stem cell, genetic testing methods, computerized patient-drug databases ,virtual drug trials and human-patient simulators can be used for the assessment of the safety of drugs, chemicals, cosmetics, medical devices, consumer and investigational products.
Imagine having a headache and not having aspirin to take, or being diabetic and not being able to take certain types of insulin (Williams 3). It seems impossible that these drugs could be unavailable to humans, but they would not be attainable had scientists not tested these drugs on non-animal subjects. Contrary to what many people believe, testing drugs on animals often give defective results. “More than 205,000 new drugs are marketed worldwide every year, most undergo the most archaic and unreliable testing methods still in use: animal studies” (PETA 1). Although animals may seem the like ideal specimens for testing new drugs, the experiments are untrustworthy and can cause unknown side effects.
Reinarman, Craig and Peter D. A. Cohen and Hendrien L. Kaal. “The Limited Relevance of Drug
Bad math in court is something that happens over and over again and because of it, many innocent victims have been jailed and punished unjustly over the years. The problem is not some sort of miscalculation, but the refusal of the court to recalculate. More than often enough, the judge refuses to reexamine the collected DNA in an investigation case. What the people of the court fail to realize at times is that probability is not a one off thing, it is something that should be repeated at least more than once and can even be repeated over and over again. The flipping of a coin is frequently used to explain this logic and will be explained in following paragraphs. Sometimes statistician will state that there is only a one in a million chance (or some other ludicrously large number) that the defendant is innocent; but then they fail to examine: what is that 1, what are the chances that the accused that that one in a million? In this paper, I will be discussing the issue of ‘bad math in court,’ why it happens and how something as simple as probability can get innocent people out of jail.
The reason we use this formula in particular is because the birthdays of 30 random people in a room are all independent events that do not rely on one another for it’s occurrence.
The Collier Encyclopedia’s definition for probability is the concern for events that are not certain and the reasonableness of one expectation over another. These expectations are usually based on some facts about past events or what is known as statistics. Collier describes statistics to be the science of the classification and manipulation of data in order to draw inferences. Inferences here can be read to mean expectations, leading to the conclusion that the two go hand in hand in accomplishing what mankind has tried to accomplish since the beginning of time – predicting the future. It is the notion of science that this is the most accurate way to predict events yet to occur and this has lead to it being the most widely accepted “fortune telling'; tool in the world today.