Q:''Use of this product may be hazardous to your health.This product contains saccharin,which has been determined to cause cancer in laboratory animals.''How might probability theory have played a part in this statement.

A:The product which has been talked of here belongs to,say,a company X.Now every company tests and tests for several number of times before bringing any product at the forefront.So,this company too experimented the product on laboratory animals,but then after several experiments it has been observed that very few animals got cancer.Now with this type an outcome this company has drawn a conclusion that if the product is used by human beings there could be a possibility of developing hazards,and as a matter of warning beforehand about the outcome they have stated such a warning with their product,in relation to the statement made they have used one word'may',that is there is a chance and the issue is not any everytime event. Now suppose they put 500 animals to test and the probability of diseased animals found is 0.006 or 3/500,that is, the probability then of safe animals is 497/500 or 0.994 which is quite high in comparison to the affected ones.Thus probability theory has helped manufacturers to come out with a new product after knowing the performance of the reaction of the particular product.

Q:When asked what they would use if they were marooned on an island with only one choice for a pain reliever,more doctors choose Bayer than Tylenol,Bufferin,or Anvil.Is this conclusion drawn from a sample or a population.
Ans:The conclusion has been drawn from population because all these are pain killers and the name of the most effective one has been taken,so all the medicines representing a whole but then the one that has been chosen is representing a part.

Coca Cola decides to alter the formula of its oldest & most popular product.How might probability theory be involved in such a decision.

If Coca Cola wants to alter the formula of one of its oldest and most popular products,then it is surely going into a decision making process.By doing this,Coca Cola would either change the colour or the flavour of the drink or both.When in this way Coca Cola is considering launching a new flavour on the market,the company needs to do a market research,the company needs to prepare a questionnaire and conduct a market survey.The involvement of the probability theory comes with the number of respondents giving positive responses or negative responses in terms of the way Coca Cola has determined to change the flavour.The financial outcome of the change should be calculated that is if the change is successful then the company will earn extra profits but if it is not the company stands to lose much more because it will spend something in its R&D(Research & Development) department.Suppose a response resulted in getting 75 positive outcomes out of every 100 people questioned then according to the theory of probality it is quite good and the company can set to launch the product.Now if we translate the response into the probability statement of getting successful,which is 75/100 or 3/4 or 0.75 (since probability is expressed either in fraction or decimal).There are many other factors which should also be taken into account while launching any new or upgraded product.

Is there really any such thing as an uncalculated risk.Explain.

In most of the cases we want success,every effort toward getting success can be termed as an event or an exercise or an activity.This piece has been intended to give an insight into the existence of uncalculated risk.And this type of an effort is also a risk taking exercise,where we run the risk of not getting successful.Risk taking abilities have shaped many success stories and spilling over of this ability has contributed to the term globalization.Life is a maximisation problem where we have various constraints,but the effort should be to maximise advantages out of the given constraints.The maximisation process is all about delving into cutting edge techniques and avoiding nonsensical stuffs.Realisation can be partial or can be full and even zero.Realising the absence of uncalculated risk is very stretched and demanding or an exacting task.Those who partially understand they do take risks because they do want to win,and they do know that winning is all about taking risks,they do also believe in calculated risk as well as in uncalculated risk,they move up the ladder step by step and they are most logical in the practical world.They do also believe in the concept of 'equally likely' or 'collectively exhaustible' that is thay might win or fail.The concept of realising fully is not at all believing that something bad will never ever happen to anyone but trying to make a living at gambling with greater respect for risk.It is very diificult to snap up profits along this route.The art of believing every risk as calculated is all about a careful inspection of one's faith before taking off and things get crowded.It also depends upon the departmentalization of some activities by one,such as how one examines starting from a low risk zone to a high risk zone,getting plenty of training,obeying laws and making sound investments.Some will categorise these activities as sensible steps when some other will take cue and learn from each of these activities and term their realisation as a sensible one.Most will term the second group at times as uncategorizable eccentrics.Convention is boring to some people and that is why they try to nurture their talent and allow them to flower.A logical path in this direction-that is we must work hard or reaearch or explore to teach or to create some way which can put us above the rules and justifies any risk taking exercise.If anyone is thinking in this way it is impossible for one to settle with what everyone else gets.This is how new rules are set and we get a path breaker.One needs to try and apply thoughts to be innovative and needs patience,but most people flee from this position because practically it is very hard to run the risk of ruin and death in order to get rich.It is really a debatable topic as to which is better-presence of satisfaction or ever hungry minds.Many avenues have been discovered with the help of advanced and sophisticated branches of Economics,Finance and Statistics,the applications have created paths to see the chaotic profits flowering into valuable revenue streams.Even if we take the case of a population and a sample,then knowing that a sample is a part and a population is a whole-so taking up a whole thing at a time is not an act of prudence and also one might get tired and inattentive while taking up a whole issue but testing or experimentation in parts reduces risks to an acceptable level because experimentation involves human risks. The fundamental understanding is all about managing risk and not minimizing it.There is nothing which cannot be calculated or incalculable ones.The concept is one should not take risks unnecessarily and one should not act on blind hunches to avoid risk.It all depends upon the person who is dealing with the risk but as such there is nothing which is known as an incalculable risk.