Final answer:
The probability that a randomly selected person is either a professor or a male from the group is calculated by summing the number of professors and the number of male teaching assistants, accounting for the overlap of male professors. The correct answer is 39/49.
Step-by-step explanation:
To find the probability that the selected person is either a professor or a male from the given group, we need to calculate the sum of the number of professors and the number of males, subtracting any overlap (since male professors are counted in both categories).
- Number of male professors: 10
- Number of female professors: 14
- Number of male teaching assistants: 15
- Number of female teaching assistants: 10
Total number of professors (both male and female): 10 + 14 = 24
Total number of males (both professors and teaching assistants): 10 + 15 = 25
Total number of people in the group: 10 + 14 + 15 + 10 = 49
SInce male professors are included in both groups we count them only once. We thus add the total number of professors to the number of male teaching assistants since we have already counted male professors:
Total count for 'professor or male': 24 + 15 = 39
The probability that a randomly selected person is a professor or a male is:
Probability = (Total count for 'professor or male') / (Total number of people in the group)
Probability = 39 / 49
Therefore, the correct answer is b) 39/49.