How to Calculate Conditional Probabilities

by Stephanie Ellen; Updated September 26, 2017
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Conditional probability is a term in probability and statistics that means one event depends upon another. For example, you might be asked to find the probability of getting a traffic ticket if you speed in a school zone, or find that an answer to a survey question was "Yes," given that the respondent was a woman. Conditional probabilities are usually asked in sentence formats, though in mathematical terminology you would write P(A|B), which means "the probability of event A, given event B."

Step 1

Find the probability of both events occurring together. You'll be given that information in the question (usually in a table). For example let's say the table states that 10 women said "Yes."

Step 2

Divide Step 1 from the total given in the table. For this example, let's say the total number of respondents were 100. Then 10/100=0.1.

Step 3

Identify the independent event from the two items given. In the example, the events are "being a woman in the survey" and "saying 'Yes'." The independent event is the one that can happen without the other. In our example, "woman" is the independent event, because "Yes" can only happen if there is someone there to speak.

Step 4

Calculate the probability of the event in Step 3 happening. In this example, the event "being a woman in the survey" might be stated in the table as 25 total women out of 100 respondents, so 25/100=0.25.

Step 5

Divide the figure from Step 2 by the figure from Step 4. 0.1/0.25=0.4.

Tips

  • Make sure you read the question carefully to identify the dependent, and independent, events. If you get these mixed up, you'll get the wrong answer.

About the Author

Stephanie Ellen teaches mathematics and statistics at the university and college level. She coauthored a statistics textbook published by Houghton-Mifflin. She has been writing professionally since 2008. Ellen holds a Bachelor of Science in health science from State University New York, a master's degree in math education from Jacksonville University and a Master of Arts in creative writing from National University.

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