What business and technical skills are critical for today's business intelligence/analytics and information management professionals? As part of InformationWeek's 2012 U.S. IT Salary Survey, business intelligence/analytics and information management professionals, both staff and managers, were asked to indicate what business and technical skills are critical to their job. The list of business and technical skills included Analyzing Data. The following table summarizes the responses to this skill:

If a professional is selected at random, what is the probability that he or she
a. Indicates analyzing data as critical to his or her job?
b. Is a manager?
c. Indicates analyzing data as critical to his or her job or is a manager?
d. Explain the difference in the results in (b) and (c).

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PROFESSIONAL POSITION ANALYZING DATA Critical Not critical Total Staff Management Total 296 83 379 216 65 281 512 148 660