There are four machines in a factory. At exactly 8 pm, when the mechanic is about to leave the factory, he is informed that two of the four machines are not working properly. The mechanic is in a hurry, and decides that he will identify the two fault ?->(Show Answer!)

1. There are four machines in a factory. At exactly 8 pm, when the mechanic is about to leave the factory, he is informed that two of the four machines are not working properly. The mechanic is in a hurry, and decides that he will identify the two faulty machines before going home, and repair them next morning. It takes him twenty minutes to walk to the bus stop. The last bus leaves at 8:32 pm. If it takes six minutes to identify whether a machine is defective or not, and if he decides to check the machines at random, what is the probability that the mechanic will be able to catch the last bus?

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By: anil on 05 May 2019 02.37 am

As the mechanic has decided to check two machines, thus if he identifies either both defective machines or both non defective, then the probability that he is able to catch the last bus is sum of the two. Thus, the possible outcomes are : (i) : Both are defective machines, probability = $$(frac{1}{2})(frac{1}{3}) = frac{1}{6}$$ (ii) : First is defective and second is non defective, probability = $$(frac{1}{2})(frac{2}{3}) = frac{1}{3}$$ (iii) : First is non defective and second is defective, probability = $$(frac{1}{2})(frac{2}{3}) = frac{1}{3}$$ (iv) : Both are non defective machines, probability = $$(frac{1}{2})(frac{1}{3}) = frac{1}{6}$$ In the first and last cases, the mechanic would have identified the defective machines in time to catch the bus. $$ herefore$$ Probability that he is able to catch the last bus = $$frac{1}{6} + frac{1}{6} = frac{1}{3}$$ => Ans - (D)

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MCQ-> I want to stress this personal helplessness we are all stricken with in the face of a system that has passed beyond our knowledge and control. To bring it nearer home, I propose that we switch off from the big things like empires and their wars to more familiar little things. Take pins for example! I do not know why it is that I so seldom use a pin when my wife cannot get on without boxes of them at hand; but it is so; and I will therefore take pins as being for some reason specially important to women.There was a time when pinmakers would buy the material; shape it; make the head and the point; ornament it; and take it to the market, and sell it and the making required skill in several operations. They not only knew how the thing was done from beginning to end, but could do it all by themselves. But they could not afford to sell you a paper of pins for the farthing. Pins cost so much that a woman's dress allowance was calling pin money.By the end of the 18th century Adam Smith boasted that it took 18 men to make a pin, each man doing a little bit of the job and passing the pin on to the next, and none of them being able to make a whole pin or to buy the materials or to sell it when it was made. The most you could say for them was that at least they had some idea of how it was made, though they could not make it. Now as this meant that they were clearly less capable and knowledgeable men than the old pin-makers, you may ask why Adam Smith boasted of it as a triumph of civilisation when its effect had so clearly a degrading effect. The reason was that by setting each man to do just one little bit of the work and nothing but that, over and over again, he became very quick at it. The men, it is said, could turn out nearly 5000 pins a day each; and thus pins became plentiful and cheap. The country was supposed to be richer because it had more pins, though it had turned capable men into mere machines doing their work without intelligence and being fed by the spare food of the capitalist just as an engine is fed with coals and oil. That was why the poet Goldsmith, who was a farsighted economist as well as a poet, complained that 'wealth accumulates, and men decay'.Nowadays Adam Smith's 18 men are as extinct as the diplodocus. The 18 flesh-and-blood men have been replaced by machines of steel which spout out pins by the hundred million. Even sticking them into pink papers is done by machinery. The result is that with the exception of a few people who design the machines, nobody knows how to make a pin or how a pin is made: that is to say, the modern worker in pin manufacture need not be one-tenth so intelligent, skilful and accomplished as the old pinmaker; and the only compensation we have for this deterioration is that pins are so cheap that a single pin has no expressible value at all. Even with a big profit stuck on to the cost-price you can buy dozens for a farthing; and pins are so recklessly thrown away and wasted that verses have to be written to persuade children (without success) that it is a sin to steal, if even it’s a pin.Many serious thinkers, like John Ruskin and William Morris, have been greatly troubled by this, just as Goldsmith was, and have asked whether we really believe that it is an advance in wealth to lose our skill and degrade our workers for the sake of being able to waste pins by the ton. We shall see later on, when we come to consider the Distribution of Leisure, that the cure for this is not to go back to the old free for higher work than pin-making or the like. But in the meantime the fact remains that the workers are now not able to make anything themselves even in little bits. They are ignorant and helpless, and cannot lift their finger to begin their day's work until it has all been arranged for them by their employer's who themselves do not understand the machines they buy, and simply pay other people to set them going by carrying out the machine maker's directions.The same is true for clothes. Earlier the whole work of making clothes, from the shearing of the sheep to the turning out of the finished and washed garment ready to put on, had to be done in the country by the men and women of the household, especially the women; so that to this day an unmarried woman is called a spinster. Nowadays nothing is left of all this but the sheep shearing; and even that, like the milking of cows, is being done by machinery, as the sewing is. Give a woman a sheep today and ask her to produce a woollen dress for you; and not only will she be quite unable to do it, but you are likely to find that she is not even aware of any connection between sheep and clothes. When she gets her clothes, which she does by buying them at the shop, she knows that there is a difference between wool and cotton and silk, between flannel and merino, perhaps even between stockinet and other wefts; but as to how they are made, or what they are made of, or how they came to be in the shop ready for her to buy, she knows hardly anything. And the shop assistant from whom she buys is no wiser. The people engaged in the making of them know even less; for many of them are too poor to have much choice of materials when they buy their own clothes.Thus the capitalist system has produced an almost universal ignorance of how things are made and done, whilst at the same time it has caused them to be made and done on a gigantic scale. We have to buy books and encyclopaedias to find out what it is we are doing all day; and as the books are written by people who are not doing it, and who get their information from other books, what they tell us is twenty to fifty years out of date knowledge and almost impractical today. And of course most of us are too tired of our work when we come home to want to read about it; what we need is cinema to take our minds off it and feel our imagination.It is a funny place, this word of capitalism, with its astonishing spread of education and enlightenment. There stand the thousands of property owners and the millions of wage workers, none of them able to make anything, none of them knowing what to do until somebody tells them, none of them having the least notion of how it is made that they find people paying them money, and things in the shops to buy with it. And when they travel they are surprised to find that savages and Esquimaux and villagers who have to make everything for themselves are more intelligent and resourceful! The wonder would be if they were anything else. We should die of idiocy through disuse of our mental faculties if we did not fill our heads with romantic nonsense out of illustrated newspapers and novels and plays and films. Such stuff keeps us alive, but it falsifies everything for us so absurdly that it leaves us more or less dangerous lunatics in the real world.Excuse my going on like this; but as I am a writer of books and plays myself, I know the folly and peril of it better than you do. And when I see that this moment of our utmost ignorance and helplessness, delusion and folly, has been stumbled on by the blind forces of capitalism as the moment for giving votes to everybody, so that the few wise women are hopelessly overruled by the thousands whose political minds, as far as they can be said to have any political minds at all, have been formed in the cinema, I realise that I had better stop writing plays for a while to discuss political and social realities in this book with those who are intelligent enough to listen to me.A suitable title to the passage would be
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