## Counting Techniques and Introduction to Probability

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CountingTechniques and Introduction to Probability

CountingTechniques and Introduction to Probability

Probabilityis a branch of mathematics and statistics that measures thelikelihood of a particular event occurring. If the probability of anevent occurring is high, there is more certainty that the event willoccur. Probability is measured by determining the ratio of thepossible number of favorable results and the total number of resultsin the set. There are numerous applications of probability in dailylife. One of the most important applications is in the insuranceindustry. The insurance company uses probability in the evaluation ofa policy. For example, in health insurance statistical data indicatethat smokers are more likely to develop serious health conditions.This is determined by comparing the incidences of serious medicalconditions among smokers with the incidences in the generalpopulation. As a result, these individuals are likely to have moreinsurance claims. Probability theory has an important implication onthe decision making process. Individuals will identical insurancepolicies are therefore likely to have different rates or premiums.This is due to the analyzable factors that are likely to affect thelikelihood of a claim (Bean, 2001). Thus, probability plays acritical role in calculation and management of risks in the insuranceindustry.

Jackpotwhere a group of six winning numbers is drawn from a set of 49numbers is the most common lottery game. There are 13,983,816 (49 x48 x 47 x 46 x 45 x 44/ 6 x 5 x 4 x 3 x 2 x 1) possible groups ofwinning numbers which can be drawn from the set. Assuming that allthe numbers have the same likelihood of being drawn, each set of sixwinning numbers has the probability of 1/13,983,816. This means thatthe probability of winning the jackpot is similar to the probabilityof flipping the coin 24 times and obtained all successful heads.

Themain difference between the probability of a given weather forecastand the probability of getting three successful heads after flippinga coin is the sample space. In flipping a coin, the sample space incountable and thus the probability is theoretical. On the other hand,the weather forecast has uncountable sample space, and thus theprobability is subjective.

References

Bean,M. (2001). Probability:the science of uncertainty with applications to investments,insurance, and engineering.Brooks/Cole.