What is a conditional probability?

Conditional probability is a term often used to describe the probability of a particular event, given that the second event occurs. This probability is expressed formally as P (A/B). A conditional probability is a mathematical concept, but is often used in scientific experiments in which they relate to two or more variable events.

In order to determine the conditional probability, the combined probability of the first and second events is divided by the probability of the second event. For example, if there are 100 people in the room, of which 25 percent have both brown and green eyes, and 40 percent of them have green eyes, a conditioned probability would be devised by 0.25 by 0.40. The result is 0.625. This means that there is a probability of 62.5 %that each individual selected from the group will have brown hair, because it has green eyes.

The conditional probability has a number of applications in many fields. The formula can easily be applications into a wide range of scientific experims to obtain important information. This information is important for medical and pharmaceutical scientists, all types of development engineers and even business analysts.

Medical and pharmaceutical scientists may use probability data in relation to reactions or drug interactions or to determine the probability that the patient will have a certain condition based on a given set of circumstances or to determine the patient's probable reaction to a certain treatment based on known variables. Engineers can use such equations in relation to the failure rate, choose the best possible materials for the project or to determine the cure time for certain types of materials. A business analyst might want to determine the probability that the customer buys a specific item, given that he already owns another particular item. This can be used to discourage the best goals for marketing and advertising campaigns.

illustrationThe results of the conditional probability are sometimes listed in Venn's diagram, which is a diagram of two or more overlapping circles. One circle represents an instance in which the first and second events occur. The second circle represents an instance in which only the second event occurs. Overlying areas are the likelihood of a second event, given that the first occurred.

calculations for situations involving more than two events or variables become much more complex. Many suggest that they can be simplified by actual numbers rather than percent or rates. A conditional probability is often the first step necessary in calculating advanced functions such as inverse probability.