Analyzing Data: Basic Probability

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What business and technical skills are critical for today's intelligence$/$analytics and information management professionals? As part of Information Week's $2014$ U$.$S$.$ IT Salary Survey, business intelligence$/$analytics and data integration$/$warehousing 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:

PROFESSIONAL POSITION

ANALYZING

DATA

Staff

Management

Total

Critical

$568$

$442$

$1010$

Not Critical

$129$

$697$

$109$

$551$

$238$

Total

$1,248$

Source: Data extracted from $"2014$ Salary Survey: BI & Analytics," InformationWeek Reports, May $2014,$ p$.35,$ reports.informationweek.com. $($Data revised$)$

a$.$ Given that a professional is staff, what is the probability that the professional indicates analyzing data as critical to their job?

b$.$ Given that a professional is staff, what is the probability that the professional indicates analyzing data is not critical to their job?

c$.$ Given that a professional is a manager, what is the probability that the professional indicates analyzing data as critical to their job?

d$.$ Given that a professional is a manager, what is the probability that the professional indicates analyzing data is not critical to their job?