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The mathematics faculty at a college consists of 12 fill professors, 10
associate professors, 10 assistant professors, and 12 teaching assistants (TAs), If or
faculty member is randomly selected, find the probability of choosing a full professor
TA.
The probability is . (Type an integer of a fraction. Simplify your answer)

Ask by Chandler Floyd. in the United States
Mar 31,2025

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The probability of choosing a full professor is .

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Mind Expander

To find the probability of choosing a full professor TA, we first need to understand the total number of faculty members and the specific groups we’re interested in.
First, let’s calculate the total number of faculty members:
  • Full professors: 12
  • Associate professors: 10
  • Assistant professors: 10
  • Teaching assistants (TAs): 12
Now, adding these numbers together, we have faculty members in total.
Next, we note that these groups are distinct, meaning there are no overlaps. Since the TAs and full professors are different roles, there are actually 0 faculty members who are both full professors and TAs.
Thus, the probability of randomly selecting a faculty member who is a full professor TA is .
Therefore, the probability is .

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