Conditional probability

The popular Monty Hall Problem is about being on a game show where you’re either going to win a fancy sports car or a goat. It’s a no brainer on which one you would prefer: the car. You have to choose between three doors. Behind two of the doors are goats and the fancy car is the last one. Whichever door you choose, the prize behind it is yours. The sample space is one thing to consider in this problem. There is a winning door and the two remaining doors are x and y and have goats behind them. If the contestant chooses door x or door y, which has the car behind it, the sample space would have nine outcomes: S ={(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}. Being the contestant, you would think that it doesn’t…

This uncertainty includes the quantities resulting from lack of sufficient information. Another important concept in Bayesian methods are the need to determine the prior probability distribution (probability distribution describing our beliefs about the uncertainty in the model before data becomes available) taking into account the available information. Generally, Bayesian methods involve the sequential application of the Bayes formula and the steps in these methods can be summarized as…

"Struck by Lightning: the curious world of probabilities" is a book written in 2005 by Jeffrey S. Rosenthal, an award-winning Canadian statistician and author. Jeffrey S. Rosenthal graduated from Woburn Collegiate Institute in 1984, received his B.Sc. in mathematics, physics and computer science in Toronto in 1988. He later received his PhD in mathematics in Harvard University in 1992. He performs music and improv. comedy as well as being an author and supervisor of student projects. "Struck by…

as numeracy. Age. Older individuals don’t understand risk information as well, both overestimate and underestimate probabilities (Fuller, Dudley, & Blacktop, 2001), worse risk comprehension than younger individuals (Fausset & Rogers, 2012). Much of the literature supports the idea that decision making effectiveness…

Taking risks is often apart of everyday life, the hard part about it is deciding to take them or not. The fictional novel Lyddie by Katherine paterson. It is all about a girl (named Lyddie) who has to work in a factory to pay off her mother’s debt but the working conditions are not that good, so she is thinking about signing a petition to try to get better working conditions, if she does she has the risk of getting blacklisted. Should she take the risk. Although some people think Lyddie should…

uncertainty. When an “outcome is the result of adding the outcomes of many separate performances, all in certain respects uniform”; in other words, when the frequency-ratio is known, then the experiment is named divisible, while a non-divisible or non-seriable experiment is one which “can be neither itself broken down into a number of uniform additive parts nor treated as part of a divisible experiment” (p. 8). In a non-divisible experiment the frequency-ratio standpoint has no actual sense. One…

There is no inventor, known contributors, and early uses. For instance, one can find the true and false values for a computer program. P(A|B) = P (A (B) / P (B) is the conditional probability representation. In additional, truth tables and probability are today uses. Bayes Theorem is the final concept in statistics, which is defined as the description of the probability of events based on related conditions. Thomas Bayes developed P (A|B) = P (B|A) (P (A) / P (B) where Pierre-Simon Laplace…

2005). In Li (2000) paper, a new random variable named ‘time-until-default’ was created to demonstrate survival time of each defaultable entity. And the copula function approach is based on this random variable to evaluate the default probability of financial instruments. Specifically, copula function specify the joint distribution of the survival times after using the market information to derive the marginal distribution of the survival time. This approach solves the default correlation and…

In definition, probability refers to the measure of the likelihood of an event happening. The probability for any event occurring falls between 1 percent and 100 percent thus meaning that the interpreted meaning of a probability equals the subject meaning held of the probability (Grinstead et al, 1997). However, it is worth noting that the application of probability or assigning of probability to the events in the effort to gratifying the axioms of probability follows some rules or basics…

Probability Warning, quit reading now if you don’t want to learn about how important probability and different parts of it are. Still reading? By the end of this paper you will be able to identify what probability is and what the different parts are, how they can be applied in the real world, and why it is important in a career. Independent Events what are they? When two events are independent of each other hints the name, this means is that one event has no effect on the other event. An example…