Probability 7

C  The Conditional Law Conditional probabilities are based on knowledge of one of the variables. The conditional probability of an event, such as X, occurring given that another event, such as Y, has occurred is expressed as: P(X|Y) = P(X and Y) / P(Y) = {P(X) . P(Y|X)} / P(Y) Note that when using the conditional law of probability, you always divide the joint probability by the probability of the event after the word given. Thus, to get P(X given Y), you divide the joint probability of X and Y by the unconditional probability of Y. In other words, the above equation is used to find the conditional probability for any two dependent events. When two events, such as X and Y, are independent their conditional probability is calculated as follows: P(X|Y) = P(X) and P(Y|X) = P(Y) For example, if a single card is selected at random from a deck of cards, what is the probability that the card is a king given that it is a club? P(king given club) = P (X|Y) = {P(X) .P(Y|X)} / P(Y) P(Y) = 13/52, and P(king given club) = 1/52, thus P(king given club) = P(X|Y) = (1/52) / (13/52) = 1/13 Note that this example can be solved conceptually without the use of equations. Since it is given that the card is a club, there are only 13 clubs in the deck. Of the 13 clubs, only 1 is a king. Thus P(king given club) = 1/13. Application of Probability In business, probability theory is used in the calculation of long-term gains and losses. This is how a company whose business is based on risk calculates "probability of profitability" within acceptable margins. An example of this is the way in which life insurance companies calculate the cost of life insurance policies and is based on how many policy holders are reasonably expected to die within a year versus revenue generated from other policies extended. In this scenario it is important to point out that in order for a company to mitigate the risk associated with loss of revenue it must issue a substantial number of policies.Ultimately the insurance company charges more when it is at risk of having to pay out. I didn't realize that insurance was inverse for health and auto, but I can see why it would be. First, to understand this concept you have to suspend the want to point out the exceptions. This being statements like, "I knew a guy that had a heart attack at 20." Statistically, things such as heart attacks in your 20s don't happen often. That being said, it might be easily shown that as your age increases your risk of sickness. Now also bear in mind that the insurance company is concerned with "how much" moreso than "how often." They are a company so they watch the bottom line. In youth you may be sick, but most likely it will not cost much. A prescription vs. surgery etc. Now coming to car insurance: It is easily shown that the younger the driver the worse the accident might be. This shows why young males are most often the worst to ensure. Statistically, the young male is prone to accidents and usually might be involved in some of the most not less expensive accidents. Older drivers tend to go slower and when there is an accident it is usually not as severe.