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: Male Female Pass 34 26 Fail 6 34 Suppose an employee is randomly selected from the 100 who took the examination. a. Find the probability that the employee either passed or was a male b. Find the probability that the employee either failed or was a female. c. Interpret the events and . d. Find the probability that the employee passed given that he was a male. e. Find the probability that the employee was male given that the employee passed. f. Are events P and M independent? g. Are events P and F independent?