Problem 48 - Algebra and Trigonometry

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 female.

Step-by-Step Solution

Answer

The probability that the selected person is a professor or a female is 0.65 or 65%.

Step 1: Calculate total number of people

First, we should sum up the total people present. The total number of people is the sum of male professors, female professors, male teaching assistants and female teaching assistants which is \(8 + 11 + 14 + 7 = 40\).

Step 2: Calculate the number of professors and females

Next, we should calculate the number of professors and the number of females. The number of professors is the sum of male and female professors which is \(8 + 11 = 19\). The number of females is the sum of female professors and female teaching assistants which is \(11 + 7 = 18\).

Step 3: Calculate the overlapping group

Now, we need to calculate the number of female professors which is the overlapping group. According to the problem, female professors are counted as 11.

Step 4: Calculate the probability

We calculate the probability by adding the probabilities of being a professor and being a female and then subtract the probability of being a female professor. This is because the group of female professors has been counted twice, once while calculating the number of professors and another time while calculating the number of females. So, the probability will be \((19/40) + (18/40) - (11/40) = 0.65\) or 65%.