Problem 47
Question
Use this information to solve Exercises \(47-48 .\) The mathematics department of a college has 8 male professors, 11 female professors, 14 male teaching assistants, and 7 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a professor or a male.
Step-by-Step Solution
Verified Answer
The probability that the selected person is a professor or a male is \(33 / 40\).
1Step 1: Identify Total Possible Outcomes
To solve this problem, first identify total number of people in the group. This is obtained by adding together all the professors and teaching assistants, which comes out as \(8 + 11 + 14 + 7 = 40 \).
2Step 2: Identify Favored Outcomes
The next step is to identify the number of outcomes where the selected person is a professor or a male. This can be calculated by adding together all the male professors, female professors, and male teaching assistants. \(8 + 11 + 14 = 33\).
3Step 3: Compute the Probability
Now, the probability that the selected person is a professor or a male can be calculated. Probability in this case is obtained by dividing the number of favored outcomes by total possible outcomes. Thus, the required probability is \(33 / 40 \).
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