Question

find the indicated probability. give your answer as a simplified fraction.
the managers of a corporation were surveyed to determine the background that
leads to a successful manager. each manager was rated as being either a good, fair,
or poor manager by his/her boss. the managers educational background was also
noted. the data appear below.
given that a manager is only a fair manager, what is the probability that this manager
has a college degree?
educational background
manager
rating
h. s.
some college
college degree
masters or ph.d.
totals
good
7
4
25
3
39
fair
6
15
43
23
87
poor
3
2
9
20
34
totals
16
21
77
46
160

Explanation:

Step1: Identify relevant data

We need the number of fair managers with a college degree and the total number of fair managers. From the table, for "Fair" rating: College Degree is 43, and total fair managers is 87.

Step2: Apply conditional probability formula

The formula for conditional probability \( P(A|B) = \frac{P(A \cap B)}{P(B)} \). Here, \( A \) is "has a college degree" and \( B \) is "is a fair manager". So \( P(\text{College Degree} | \text{Fair}) = \frac{\text{Number of fair managers with college degree}}{\text{Total number of fair managers}} = \frac{43}{87} \).

Answer:

\(\frac{43}{87}\)