Probability
The word probability may have varying meaning as applied in the different field. However, two of those meaning is important for the development and application of the mathematical theory of probability. The meaning of probability in this field is focused on the interpretation of probability as relative frequencies, in which simple games such as coins, card, dice, and roulette wheels outcomes could be predicted.
History of Probability
In French Society in the 1650’s, gambling was popular and fashionable, with no restriction by the government laws. As the games become more complex and stake becomes higher, many suggested that there is a need for a mathematical method for computing the chance of a win. A well-known gambler, chevalier De Mere consulted the famous mathematician, Blaise Pascal in Paris to ask some question concerning games chances. Pascal began to relate this question to his friend and colleague Pierre Fermat. The correspondence between Pascal and Fermat originated into the mathematical study of probability.
Theory of Probability
The probability theory is a branch of mathematics which deals with the analysis and evaluation of random phenomena. The outcome of a random event could not be possibly predicted before it occurs, however, its outcome may be one of the several possible outcomes that have occurred. Thus, the actual outcome is considered to be determined by a mere chance.
How is calculated
The method for calculating and computing probability is known as the classical method. Suppose a game has n like an outcome, in which m outcomes correspond to winning. The probability of winning is predicted as m/n
Advantages

  • It is convenience and ease of use.
  • It creates samples that are the true representative of the population.
  • It helps creates strata, group or layers that are the true representative of strata, group or layers in the population.
  • It also creates samples that are the true representative of the population and does not possibly need a random number generator.

Disadvantages

  • Might not work well if unit members are not of the same quantity.
  • Difficult and time-consuming when creating larger samples.

Objectivists and Subjectivists are the two major categories of probability interpretation, whose adherents possess conflicting views about the functional nature of probability.
Objectivists is an interpretation of probability which assigns numbers to describe objectives and physical state of affairs while Subjectivists is an interpretation of probability also assign numbers per subjective probability as a degree of belief.
Objective probability is a probability interpretation that predicts event outcome based on a measure of a recorded observation, for example, an event recorded that tossing a coin in the air that the head occur more than the tail. While the subjective probability is a probability interpretation that predicts the outcome of an event based on personal judgment of an individual. An example is a football game; the winner could be predicted based on individual knowledge and perceptions on the team.
 

Age Group Tested Never Tested
18-44 years 50,080 56,405
45-64 years 23,768 48,537
65-74 years 2,694 15,162
75 years and older 1,247 14,663
Total 77,789 134,767

 
Expressing the Table in percentage where Total population, n is 77,789 + 134,767 = 212,556.
Each outcome is expressed as m, Hence probability is m/n, i.e. 50,080/ 212,556 = 0.24.

Age Group Tested Never Tested
18-44 years 0.24 0.27
45-64 years 0.11 0.23
65-74 years 0.01 0.07
75 years and older 0.01 0.06
Total 0.37 0.63

 

  1. Based on the above survey, the probability that randomly selected American has never been tested

=p(NT) / p(NT) + p(T)
0.63 / 0.63 + 0.37
0.63 / 1 = 0.63

  1. The probability that 18-44 years old American has never been tested

=p(NT) / p(NT) + p(T)
0.27 / 0.27 + 0.24
0.27 / 0.51 = 0.51