Question

question 11
a union executive conducted a survey of its members to determine what the membership
felt were the important issues to be resolved during upcoming negotiations with
management. the results indicate that 74% of members felt that job security was an
important issue. 45% indicated pension benefits as an important issue.
considering only those who felt that pension benefits were important, 60% also felt that
job security was an important issue. what is the probability that at least one of these two
issues is important?
show all work.

Explanation:

Step1: Identify the formula

Use the formula for the probability of the union of two events \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event that job - security is important (\(P(A) = 0.74\)) and \(B\) be the event that pension benefits is important (\(P(B)=0.45\)), and \(P(A\cap B) = 0.60\).

Step2: Substitute the values into the formula

Substitute \(P(A) = 0.74\), \(P(B)=0.45\) and \(P(A\cap B) = 0.60\) into \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).

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Answer:

The probability that at least one of these two issues is important is \(0.59\)