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 \( \square \). (Type an integer or a fraction. Simplify your answer.)

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: \[ \text{Total faculty} = 5 + 5 + 4 + 10 = 24 \] Next, we find the number of successful outcomes, which includes the full professors and TAs: \[ \text{Successful outcomes} = \text{Full professors} + \text{Teaching assistants} = 5 + 10 = 15 \] Now we can find the probability: \[ \text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total number of faculty}} = \frac{15}{24} \] Simplifying this gives: \[ \frac{15 \div 3}{24 \div 3} = \frac{5}{8} \] So, the probability is \( \frac{5}{8} \).