A number is chosen at random among the first 120 natural numbers. The probability of the number chosen being a multiple of 5 or 15 is ?->(Show Answer!)

1. A number is chosen at random among the first 120 natural numbers. The probability of the number chosen being a multiple of 5 or 15 is

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MCQ-> Analyze the following passage and provide appreciate answers for the questions that follow. Ideas involving the theory probability play a decisive part in modern physics. Yet we will still lack a satisfactory, consistence definition of probability; or, what amounts to much the same, we still lack a satisfactory axiomatic system for the calculus of probability. The relations between probability and experience are also still in need of clarification. In investigating this problem we shall discover what will at first seem an almost insuperable objection to my methodological views. For although probability statements play such a vitally important role in empirical science, they turn out to be in principle impervious to strict falsification. Yet this very stumbling block will become a touchstone upon which to test my theory, in order to find out what it is worth. Thus, we are confronted with two tasks. The first is to provide new foundations for the calculus of probability. This I shall try to do by developing the theory of probability as a frequency theory, along the lines followed by Richard von Mises, But without the use of what he calls the ‘axiom of convergence’ (or ‘limit axiom’) and with a somewhat weakened ‘axiom of randomness’ The second task is to elucidate the relations between probability and experience. This means solving what I call the problem of decidability statements. My hope is that the investigations will help to relieve the present unsatisfactory situation in which physicists make much use of probabilities without being able to say, consistently, what they mean by ‘probability’.The statement, “The relations between probability and experience are still in need of clarification” implies that:
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MCQ->A number is chosen at random among the first 120 natural numbers. The probability of the number chosen being a multiple of 5 or 15 is....

MCQ-> Read the following passage and provide appropriate answers for the questionsThere is an essential and irreducible ‘duality’ in the normative conceptualization of an individual person. We can see the person in terms of his or her ‘agency’, recognizing and respecting his or her ability to form goals, commitments, values, etc., and we can also see the person in terms of his or her ‘well-being’. This dichotomy is lost in a model of exclusively self- interested motivation, in which a person’s agency must be entirely geared to his or her own well-being. But once that straitjacket of self-interested motivation is removed, it becomes possible to recognize the indisputable fact that the person’s agency can well be geared to considerations not covered - or at least not fully covered - by his or her own well-being. Agency may be seen as important (not just instrumentally for the pursuit of well-being, but also intrinsically), but that still leaves open the question as to how that agency is to be evaluated and appraised. Even though the use of one’s agency is a matter for oneself to judge, the need for careful assessment of aims, objective, allegiances, etc., and the conception of the good, may be important and exacting. To recognize the distinction between the ‘agency aspect’ and the ‘well-being aspect’ of a person does not require us to take the view that the person’s success as an agent must be independent, or completely separable from, his or her success in terms of well-being. A person may well feel happier and better off as a result of achieving what he or she wanted to achieve - perhaps for his or her family, or community, or class, or party, or some other cause. Also it is quite possible that a person’s well-being will go down as a result of frustration if there is some failure to achieve what he or she wanted to achieve as an agent, even though those achievements are not directly concerned with his or her well-being. There is really no sound basis for demanding that the agency aspect and the well-being aspect of a person should be independent of each other, and it is, I suppose, even possible that every change in one will affect the other as well. However, the point at issue is not the plausibility of their independence, but the sustainability and relevance of the distinction. The fact that two variables may be so related that one cannot change without the other, does not imply that they are the same variable, or that they will have the same values, or that the value of one can be obtained from the other on basis of some simple transformation. The importance of an agency achievement does not rest entirely on the enhancement of well-being that it may indirectly cause. The agency achievement and well-being achievement, both of which have some distinct importance, may be casually linked with each other, but this fact does not compromise the specific importance of either. In so far as utility - based welfare calculations concentrate only on the well- being of the person, ignoring the agency aspect, or actually fails to distinguish between the agency aspect and well-being aspect altogether, something of real importance is lost.According to the ideas in the passage, the following are not true expect:
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MCQ-> People are continually enticed by such "hot" performance, even if it lasts for brief periods. Because of this susceptibility, brokers or analysts who have had one or two stocks move up sharply, or technicians who call one turn correctly, are believed to have established a credible record and can readily find market followings. Likewise, an advisory service that is right for a brief time can beat its drums loudly. Elaine Garzarelli gained near immortality when she purportedly "called" the 1987 crash. Although, as the market strategist for Shearson Lehman, her forecast was never published in a research report, nor indeed communicated to its clients, she still received widespread recognition and publicity for this call, which was made in a short TV interview on CNBC. Still, her remark on CNBC that the Dow could drop sharply from its then 5300 level rocked an already nervous market on July 23, 1996. What had been a 40-point gain for the Dow turned into a 40-point loss, a good deal of which was attributed to her comments.The truth is, market-letter writers have been wrong in their judgments far more often than they would like to remember. However, advisors understand that the public considers short-term results meaningful when they are, more often than not, simply chance. Those in the public eye usually gain large numbers of new subscribers for being right by random luck. Which brings us to another important probability error that falls under the broad rubric of representativeness. Amos Tversky and Daniel Kahneman call this one the "law of small numbers.". The statistically valid "law of large numbers" states that large samples will usually be highly representative of the population from which they are drawn; for example, public opinion polls are fairly accurate because they draw on large and representative groups. The smaller the sample used, however (or the shorter the record), the more likely the findings are chance rather than meaningful. Yet the Tversky and Kahneman study showed that typical psychological or educational experimenters gamble their research theories on samples so small that the results have a very high probability of being chance. This is the same as gambling on the single good call of an advisor. The psychologists and educators are far too confident in the significance of results based on a few observations or a short period of time, even though they are trained in statistical techniques and are aware of the dangers.Note how readily people over generalize the meaning of a small number of supporting facts. Limited statistical evidence seems to satisfy our intuition no matter how inadequate the depiction of reality. Sometimes the evidence we accept runs to the absurd. A good example of the major overemphasis on small numbers is the almost blind faith investors place in governmental economic releases on employment, industrial production, the consumer price index, the money supply, the leading economic indicators, etc. These statistics frequently trigger major stock- and bond-market reactions, particularly if the news is bad. Flash statistics, more times than not, are near worthless. Initial economic and Fed figures are revised significantly for weeks or months after their release, as new and "better" information flows in. Thus, an increase in the money supply can turn into a decrease, or a large drop in the leading indicators can change to a moderate increase. These revisions occur with such regularity you would think that investors, particularly pros, would treat them with the skepticism they deserve. Alas, the real world refuses to follow the textbooks. Experience notwithstanding, investors treat as gospel all authoritative-sounding releases that they think pinpoint the development of important trends. An example of how instant news threw investors into a tailspin occurred in July of 1996. Preliminary statistics indicated the economy was beginning to gain steam. The flash figures showed that GDP (gross domestic product) would rise at a 3% rate in the next several quarters, a rate higher than expected. Many people, convinced by these statistics that rising interest rates were imminent, bailed out of the stock market that month. To the end of that year, the GDP growth figures had been revised down significantly (unofficially, a minimum of a dozen times, and officially at least twice). The market rocketed ahead to new highs to August l997, but a lot of investors had retreated to the sidelines on the preliminary bad news. The advice of a world champion chess player when asked how to avoid making a bad move. His answer: "Sit on your hands”. But professional investors don't sit on their hands; they dance on tiptoe, ready to flit after the least particle of information as if it were a strongly documented trend. The law of small numbers, in such cases, results in decisions sometimes bordering on the inane. Tversky and Kahneman‘s findings, which have been repeatedly confirmed, are particularly important to our understanding of some stock market errors and lead to another rule that investors should follow.Which statement does not reflect the true essence of the passage? I. Tversky and Kahneman understood that small representative groups bias the research theories to generalize results that can be categorized as meaningful result and people simplify the real impact of passable portray of reality by small number of supporting facts. II. Governmental economic releases on macroeconomic indicators fetch blind faith from investors who appropriately discount these announcements which are ideally reflected in the stock and bond market prices. III. Investors take into consideration myopic gain and make it meaningful investment choice and fail to see it as a chance of occurrence. IV. lrrational overreaction to key regulators expressions is same as intuitive statistician stumbling disastrously when unable to sustain spectacular performance.....

MCQ-> Analyse the following passage and provide an appropriate answer for the questions that follow. When we speak of the “probability of death”, the exact meaning of the experience can be defined in the following way only. We must not think of an individual, but of this expression can be defined in the following way only. We must not think of an individual, but of a certain class as a whole, e.g., “all insured men forty-one years old living in a given country and not engaged in certain dangerous occupations.” A probability of death is attached to the class of men or to another class that can be defined in a similar way. We can say nothing about the probability of death of an individual even if we know this condition of life and health in detail. The phrase “probability of death”, which it refers to a single person, has no meaning at all.Which of the following conclusions can be drawn from the passage? 1. Singular, non replicable events can be assigned numerical probability value. 2. Probability calculation requires data of the class of people or of events. 3. The data about a class of events can be used to predict the future of any specific event.....