4.53 A proficiency examination for a certain skill was given to 100 employees of a firm. Forty of the employees were male. Sixty of the employees passed the examination, in that they scored above a preset level for satisfactory performance.

The breakdown among males and females was as follows:

Suppose an employee is randomly selected from the 100 who took the examination.
a Find the probability that the employee passed given that he was a male.
b Find the probability that the employee was male given that the employee passed.
c Are events P and M independent?
d Are events P and F independent?
e Constructed and interpret a meaningful odds ratio for these data.

Pass P Fail P Male M Female F 24 36 16 24