Question

The mathematics faculty at a college consists of 6 full​ professors, 9 associate​ professors, 12 assistant​ professors, and 7 teaching assistants​ (TAs). If one faculty member is randomly​ selected, find the probability of choosing a full professor or a TA.
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Part 1
The probability is
  
enter your response here. ​(Type an integer or a fraction. Simplify your​ answer.)

Answer 1

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 and the number of successful outcomes (choosing either a full professor or a TA).

1. **Count the total number of faculty members**:

\[
\text{Total faculty} = \text{Full professors} + \text{Associate professors} + \text{Assistant professors} + \text{TAs}
\]
\[
\text{Total faculty} = 6 + 9 + 12 + 7 = 34
\]

2. **Count the successful outcomes**:

The successful outcomes for choosing a full professor or a TA are:
- Number of full professors = 6
- Number of teaching assistants = 7

\[
\text{Successful outcomes} = \text{Full professors} + \text{TAs} = 6 + 7 = 13
\]

3. **Calculate the probability**:

The probability \( P \) of choosing a full professor or a TA is given by the ratio of the number of successful outcomes to the total number of faculty members.

\[
P(\text{full professor or TA}) = \frac{\text{Successful outcomes}}{\text{Total faculty}} = \frac{13}{34}
\]

So, the probability of randomly selecting a full professor or a TA is:

\[
\frac{13}{34}
\]