uestion Set B1. Defineprobability and give examples. What are other terms used to describeprobability? Probability is abranch of mathematics that deals with calculating the vraisemblance of a givenevent’s occurrence, which is expressed as a number between 1 and 0.

An eventwith a probability of 1 can be considered a certainty For example · Most probably it will rain today · Chances are high that the prices ofpetrol will go up.· I doubt that he will win the race.Terms of Probability. Theprobability of a coin toss resulting in either “heads” or”tails” is 1, because there are no other options, assuming the coinlands flat. An event with a probability of .

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5 can be considered to have equalodds of occurring or not occurring: for example, the probability of a coin tossresulting in “heads” is .5, because the toss is equally as likely toresult in “tails.” An event with a probability of 0 can be consideredimpossibility2. Whatis probability theory?Probability theory is the branchof mathematics concernedwith probability. Although there are severaldifferent probability interpretations, probabilitytheory treats the concept in a rigorous mathematical manner by expressing itthrough a set of axioms. Typically these axioms formaliseprobability in terms of a probabilityspace, which assigns a measure taking values between 0 and1, termed the probability measure, to a set of outcomescalled the sample space. Any specified subset of theseoutcomes is called an event.

Centralsubjects in probability theory include discrete and continuous randomvariables, probability distributions, and stochastic processes, which providemathematical abstractions of non-deterministic oruncertain processes or measured quantities thatmay either be single occurrences or evolve over time in a random fashion.Althoughit is not possible to perfectly predict random events, much can be said abouttheir behaviour. Two major results in probability theory describing suchbehaviour are the law of large numbers and the central limit theorem. 3. What happens when combiningprobabilities? When is this used? 4. What does conditionalprobability mean? Conditionalprobability is the likelihood of an event or outcome occurring based on theoccurrence of a previous event or outcome. Conditional probability iscalculated by multiplying the probability of the preceding event by the updatedprobability of the succeeding,orconditional,event.

5 What is meant by probabilitydistribution? A probability distribution is a statistical function thatdescribes all the possible values and likelihoods that a randomvariable can take within a given range. This range will bebetween the minimum and maximum statistically possible values, but where thepossible value is likely to be plotted on the probability distribution dependson a number of factors. These factors include the distribution’s mean, standarddeviation, skewness and kurtosis.

6 Explain3 types of risk assessment data. Provide examples. 7 How are failure ratesdetermined? Failure rates arean important consideration in engineering. They are used to determine thereliability of a system or a component in a system. To calculate a failurerate, we need to observe the system or the component and record the time ittakes to break down. As with any statistic, the more data we have, the moreaccurate the failure rate calculation will be.

For example, if we werecalculating the failure rate of a specific type of USB cable, our calculationwould be more accurate if you tested 1,000 cables over a year rather than onecable over a few days. 8 What is the probability of being injured byusing a chain saw? Being murdered? Dying in an explosion? Are theseprobabilities significant? Explain? 9 Why is developing reliable data on human behaviour difficult? What isthe solution? 10 Explainthe Delphi method. The Delphi method isa forecasting method based on the results of questionnaires sent to apanel of experts.

Several rounds of questionnaires are sent out, and theanonymous responses are aggregated and shared with the group after each round.The experts are allowed to adjust their answers in subsequent rounds. Sincemultiple rounds of questions are asked and the panel is told what the groupthinks as a whole, the Delphi method seeks to reach the correct responsethrough consensus.TheDelphi method is a forecasting method based on the results of questionnaires sent to apanel of experts. Several rounds of questionnaires are sent out, and theanonymous responses are aggregated and shared with the group after each round.The experts are allowed to adjust their answers in subsequent rounds.

Sincemultiple rounds of questions are asked and the panel is told what the groupthinks as a whole, the Delphi method seeks to reach the correct responsethrough consensus.The Delphi Method communication structure https://sciencing.com/calculate-failure-rates-6403358.htmlhttps://www.investopedia.com/terms/c/conditional_probability.asphttps://www.investopedia.com/terms/p/probabilitydistribution.asphttps://en.wikipedia.org/wiki/Probability_theoryhttp://www.math-only-math.com/probability.htmlhttps://www.investopedia.com/terms/d/delphi-method.asp