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# What Is Conditional Probability?

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• Written By: Maggie Worth
• Edited By: Jenn Walker
2003-2019
Conjecture Corporation
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Conditional probability is a term often used to describe the likelihood of a specific event, given that a second event occurs. This probability is expressed formulaically as P(A/B). Conditional probability is a mathematical concept, but it is often used in scientific experiments in which two or more event variables are concerned.

In order to figure conditional probability, the combined probability of the first and second event is divided by the probability of the second event. For example, if there are 100 people in a room, 25 percent of whom have both brown hair and green eyes, and 40 percent of whom have green eyes, the conditional probability would be figured by dividing 0.25 by 0.40. The result is 0.625. This means that there is a 62.5 percent probability that any given individual selected from the group will have brown hair, given that he or she has green eyes.

Conditional probability has a number of applications across many fields. The formula can easily be applied to a wide variety of scientific experiments in order to obtain important information. Such information is important to medical and pharmaceutical researchers, all types of development engineers and even business analysts.

Medical and pharmaceutical researchers might use probability data in relationship to drug reactions or interactions to determine the likelihood of a patient having a certain condition based on a given set of circumstances, or to determine a patient's probable reaction to a certain treatment based on known variables. Engineers might use such equations in relationship to failure rates, to choose the best possible materials for a project or to determine cure times for certain types of materials. A business analyst might want to determine the probability of a customer purchasing a specific item, given that he already owns another specific item. This can be used to help determine the best targets for marketing and advertising campaigns.

Illustration of conditional probability results are sometimes presented in a Venn diagram, which is a diagram of two or more overlapping circles. One circle represents the instances in which both the first and second event occur. The other circle represents the instances in which only the second event occurs. The overlapping areas represent the probability of the second event occurring, given that the first has occurred.

Calculations for situations involving more than two events or variables become far more complex. Many suggest they may be simplified by using actual numbers rather than percentages or rates. Conditional probability is often the first step necessary in computing advanced functions, such as inverse probability.