# Conditional Probability

Statistics and probability are correlated mathematical areas which are associated with the analysis of the relative frequency of events. The two areas work together through the integration of their provisions and alignment of their arithmetic view of events. Both of them are mathematical disciplines, and hence they share the numerical aspect of looking at events (Benjamin & Cornell, 2014). Probability predicts the likelihood of events happening whereas statistics analyze the frequency of events that have passed. In this sense, statistics work as a continuation of what probability started. The field of statistics in this sense measures the accuracy with which probabilistic projections were made in the past. Probability is mainly a theoretical approach to mathematics, and its studies largely involve the consequences associated with mathematical definitions (Benjamin & Cornell, 2014). On the other hand, statistics is an applied scope of mathematics which attempts to draw a sense of observations in real-life situations. The association between the two areas of mathematics is that of projection and reality.

Both probability and statistics are pertinent and useful in the real world. However, they are different and comprehending the different is important in the interpretation of mathematical evidence (Benjamin & Cornell, 2014). A good example of conditional probability is the projection of 2018 FIFA World Cup. There were probabilistic projections obtained through model-oriented averaging of quoted winning odds for teams across different bookmakers. Probabilistic projections indicated that Brazil was the favorite candidate to win the tournament. Statistical records showed that the country was in a relatively strong position to win while France was ranked at a possible position four. The reality on the ground depended on team abilities, and France went ahead to win the tournament. Statistically, Brazil has won the highest number of World Cup tournaments, and so there was a high probability that it could win in this year’s competition. On the other hand, France had won once and so the country’s probability to win a second tournament was limited. However, it was statistically evident that France had been achieving better results than Brazil on the international ranking and went ahead to win the tournament against odds.

Conditional probability measures the likelihood of a situation on condition that another event materializes. For instance, the event of interest could be A, and B is assumed to have taken place, the conditional likelihood of occasion A, assumed the incidence of B is written as *P*(*A*|*B*). Conditional probability is an important figure in different domains such as diagnostics, prediction, classification, prediction, decision theory, and other situations (Uttley, 2016). People make predictions, classification, and predictions on the basis of different pieces of evidence. For this reason; the information that a person desires to acquire is the probability of the result on the condition of the evidence *P*(*A*|*B*).

Using classification as an example, the evidence is the features or values of measurements on which the categorization is founded. The probable results are the possible categories. However, the conditional probability is challenging to estimate from direct experiment because there are huge amounts of values that features can take (Uttley, 2016). For this reason; there would be a high number of conditional probabilities to project. Conditional probability is important in reacting to situations where people either avoid or facilitate a recurrence of certain events. Business organizations use conditional probabilities to work with economic fluctuations and avoid potentially huge losses in the long run (Uttley, 2016). The firms also apply the concept to add their chances of achieving high profitability in different financial years.