Trident University International

Javidi Thomas

Module 3: Case Assignment

BHS220: Introduction to Health Statistics

Dr. Sharleen Goalies

January 31, 2018









Probability Theory

The probability theory is a branch of mathematics that is used to determine the likelihood of an event occurring. The probability theory emerged during the 17th century when mathematicians tried to develop a formula to predict odds of winning in gambling. Initially, the theory was used to calculate the likelihood of discrete events to occur. However, it was later developed to incorporate the continuous variable. Also, probability theory can be used to determine the likelihood of discrete variables, continuous variables or a combination of both. In addition, the discrete probability is used to determine the likelihood of countable sample variables such as decks of cards (Gillies, 2012). On the other hand, continuous probability deals with continuous variables. The likelihood of an event to occur is calculated by dividing the possible number of events with the outcomes (Gillies, 2012). Subsequently, the advantage of the probability theory is that each member of a population an equal a known chance of being selected. Therefore, the selected sample is a better representative of the population (Gillies, 2012). On the other hand, the limitation of the probability theory is the impact of randomness which may result in inaccurate results. Also, an individual may input incorrect values in order to manipulate the results.

Two Categories of Probability Interpretations

The first category is subjective probability, it is based on personal judgment regarding the likelihood of an event occurring. It differs from one person to another. Also, the outcome is highly biased due to personal judgment (Gillies, 2012). The second category is known as the objective probability. Objective probability is based on recorded observation (Gillies, 2012). The objective probability is the most commonly used since it is more reliable since the results are not affected by personal bias. Therefore, objective probabilities provide more accurate results than subjective probabilities.

The data in Table 1 below represents data from 2012 National Health Interview Survey. The data shows the respondents have ever been tested or they have never been tested for HIV.

Age Group Tested (thousands) Never Tested (thousands)
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


Table 1- Adult Americans tested and not tested for HIV

The probability that Randomly Selected Adults have never been tested

The probability of randomly selecting an untested adult from the data is calculated by dividing the total number of tested adults with the total of both tested and untested. The computation is as follows; P(77,789)/(P (77,789) +P(134,767) =0.63. The results show that 63% of adult Americans have never been tested for HIV. Therefore, the probability of selecting an adult American who has been tested for HIV is (1-0.63=0.47) or 47%.

Proportion of adults of 18-44 years who have never been tested

The proportion of the untested group of 18-44 years is calculated by dividing the tested individuals in the group by the total number of those tested and untested. Therefore, the proportion= P(50,080)/(P50,080+P(56,405) = 0.47. This means that 47% of adults in the group have never been tested for HIV. According to the results, more people in the group of 18-44 years have been tested for compared to the total American adults. The study provides useful information about the proportion of the adults who have or never been tested for HIV in the U.S.

















Gillies, D. (2012). Philosophical Theories of Probability. New York: Routledge

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