Some of us have the capability of predicting what is likely to happen and what is not. Teachers with some experience can tell who and who are going to pass an examination. Sometimes they also go wrong when a bright student fails the examination. Astrologers have mastered the art of predicting the future. They will tell you whether you are going to be a lawyer or a doctor. They read your horoscope or your palm before making such predictions. Some of their predictions may come true.
In daily life we make countless decisions based on intuitive, commonsense estimates of probability. Most of the time, such estimates are fairly reliable. However, we have experienced all sorts of curious situations in which the actual probabilities differ startlingly from what we expect. You may have met pharmacists or paramedical men whose ambition was to become doctors. Then there are people who had never expected to hold high posts enjoying their windfalls.
The word “probability” has several meanings. According to the dictionary, probability means the likelihood of something happening. During the previous Presidential election there was a strong probability that a particular candidate would be the winner. Probability theory is a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined accurately before it occurs, but you may be able to guess several possible outcomes. The actual outcome, however, is determined by chance.
Relative frequencies
The experts in probability theory interpret probabilities as relative frequencies for which simple games involving coins, cards, dice and roulette wheels provide examples. If you walk into a casino, the distinctive feature of its games of chance is that the outcome of any of them cannot be predicted with certainty. However, the collective results of a large number of trials will display some regularity. The probability of “heads” in tossing a coin frequently equals one half according to the relative frequency interpretation.
The probability theory came into being when a gambler asked Blaise Pascal, the eminent French mathematician and philosopher, how to calculate the odds on certain dice throws. Since then probability theory has become one of the fastest growing branches of mathematics.
Today physicists use it to compute the probable path of a neutron through heavy water while geneticists try to determine the likelihood that a married couple would have blue-eyed children. It is difficult to think of a profession in which probability theory is not applicable. Even businessmen and politicians depend heavily on it.
When you have to meet someone on the tenth floor of a building, you have to use the lift. If you are waiting for the lift, most of the elevator cars are likely to be somewhere above you. Conversely, if you are on the tenth floor, most of the elevator cars are likely to be below you. Intuitively, on any floor, you feel that an up-moving elevator is just as likely to arrive as a down-moving one, but you cannot be sure of it.
First prize
Most of us buy sweep tickets with the hope of winning a prize. However, we always win a paltry Rs 20. Recently a woman who won the first prize of a lottery running into Rs. 24 million claimed that she had been buying sweep tickets for 24 years without winning any substantial prize. This clearly shows that winning a lottery prize is highly improbable. There is no guarantee that you will win a big prize every time you buy a sweep ticket. It is a kind of respectable gamble. You lose most of the time and win a prize very rarely. If you think that you can win a prize every time you buy a sweep ticket, your grasp of probabilities is flawed.
What is the probability that if a family has three children – two daughters and a son - who will do well in their studies? However much you encourage them to study, at least one child is likely to fail. You can only satisfy yourself in the belief that everything happens according to karmic forces.
Another way of going wrong when estimating probabilities is to assume that certain events are related when they are not. You may imagine that a flipped coin will come up heads several times in a row, but the odds will favour tails on the next flip. It does not happen that way.
No matter how many times a coin lands heads, the probability of heads on the next flip remains half. Dozens of ridiculous systems for playing games of chance are based on the “gamblers’ fallacy” that previous results have an effect on future results. The best course of action you can take is to avoid wasting your hard-earned money on games of chance.
A diehard gambler will not listen to advice and he will bet you at even odds, for example, that of the licence plates on the next 20 passing vehicles, at least two will match each other in their last digits. It sounds like a good bet. However, the odds actually are seven to one in his favour.
Small world
When you go abroad sometimes you will meet someone known to you quite accidentally. Astounded, he will say, “It’s a small world!” Indeed we are living in a global village. Technology has cut through wide distances. Social scientists at Massachusetts Institute of Technology found in a study that the average person in the United States is in direct touch with 500 people. Each person is a link in many different chains of acquaintances. They have calculated that if you pick two Americans at random, the chances are about one in 200,000 that they will know each other.
The small-world was closely studied by psychologist Stanley Milgram who selected a random group and each person was given a document and was told to mail it to an acquaintance who seemed to know the target person – the wife of a divinity student in Cambridge. The acquaintance would then send it on to one of his acquaintances and the chain would continue until it reached the target. After four days a man approached the target person and handed over the document. In the study the number of persons involved in the chain ranged from two to ten but many people believed that such a chain would require at least 100 people. The study explained how gossip becomes known around the country very fast.
A callow youth once consulted a well-known palmist before sitting his final examination in laws. The palmist read his palm, spent some time doing calculations and asked the youth what he was doing at the time. He told the palmist that he was a final year law student.
The palmist at once started working on probability theory. He said, “You are definitely going to pass the final examination. After becoming a lawyer you will launch your career in politics. Mark my words, you are going to be a minister!” The youth was so happy that he paid the palmist an additional amount. The palmist is no longer among the living. However, the youth did not pass the final examination in laws and found a job in a government department.