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The mathematics feculty at a college consists of 5 fill professors, 5 associate professors, 4
assistant professors, and 10 teaching assistants (TAs). If one feculty member is
randomly selected, find the probability of chocsing afull professor or a TA.
The probability is . (Type an integer or a fraction. Simplify your answer.)

Ask by Turner Peters. in the United States
Mar 17,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The probability is .

Solution

Let the total number of faculty members be the sum of all categories:
The favorable outcomes (selecting a full professor or a TA) are:
Thus, the probability is:
The probability is .

Answered by UpStudy AI and reviewed by a Professional Tutor

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Explain
Simplify this solution

Mind Expander

To find the probability of choosing a full professor or a teaching assistant (TA), we first need to determine the total number of faculty members.
The total faculty consists of:
  • Full professors: 5
  • Associate professors: 5
  • Assistant professors: 4
  • Teaching assistants: 10
Calculating the total:
Next, we find the number of successful outcomes, which includes the full professors and TAs:
Now we can find the probability:
Simplifying this gives:
So, the probability is .

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