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.