Probability of Selecting a Person from a Group or Committee

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Probability of selecting a person from a group or committee
Committee problems are common in probability.

Problems about picking people from groups or committees are extremely common types of questions in probability and statistics. This article shows you the odds of picking a certain person FROM a committee.

If you want to figure out possibilities for choosing people FOR committees, you’ll want to check out our articles on figuring out combinations, like this one: 5 Choose 3.


Sample problem: At a school board meeting there are 9 parents and 5 teachers. Two teachers and 5 parents are female. If a person at the school board meeting is selected at random, find the probability that the person is a parent or a female.

Step 1: Make a chart of the information. In the sample question, we’re told that we have 5 female parents, 2 female teachers, 9 total parents and 5 total teachers.

committee probability 1

Step 2: Fill in the blank column(s). For example, we know that if we have 9 total parents and 5 are female, then 4 must be male.

committee probability 2
Step 3: Add a second total to your chart to add up the columns.

committee probability 3

Step 4: Add up the probabilities. In our case we were asked to find out the probability of the person being a female or a parent. We can see from our chart that the probability of being a parent is 9/14 and the probability of being a female is 7/14.

9/14 + 7/14 = 16/14

Step 5:Subtract the probability of finding both at the same time. In our case, we subtract female parents.

committee probability 4

16/14 – 5/14 = 11/14

You’re done with the Probability of selecting a person from a group or committee!

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