Probability - And Business Decisions!

Studying statistics is an interesting endeavor as business activities are so closely related to observation, formulation of strategies and extrapolation for analysis of data and implementation of new strategies. The behavior of large groups of people can be as random as coin tosses as mentioned in the previous post. In fact the entire life insurance business is based on this fact. We can't predict whether a specific person will die next year (except for my mother who can predict deaths through dreams...no pun intended she seriously can.) But if we observe millions of people, deaths are random. Hence make accurate prediction models for payouts. The proportion of men aged 25 to 34 who will dice next year is about 0.0021 say on the North American continent. When you have this data compared to the probability of death in women which about 0.0007 for the same range an insurance company tat sells many policies to people aged 25 to 345  will have to pay off on about 0.21% of the polices sold to men and about 0.07% of the policies sold to women.

So we see the law of large numbers applies as the mean of a fairly accurate sample moves towards the mean of the population (in this case the overall customers) very slowly. The law of large numbers is the foundation of such business enterprises like gambling casinos and insurance companies.The winnings (or losses) of a gambler on a few plays are uncertain - that's why gambling is exciting. If you take 100 gamblers and make 100 observations the mean of the sample is not very close to mean of the population, it is only in the very long run that the mean outcome is predictable. The house plays tens of thousands of times so the the house unlike individual gamblers can count on the long run-regularity described by the law of large numbers. Hence the average winnings the house on tens of thousands of plays will be very close to the mean of the distribution of winnings which translates effectively to say that the mean guarantees the house a profit and that's why gambling like insurance is usually a profitable business. At the end of the day the odds are always stacked up against the consumer. 

Thoughts, 

Sam Kurien