MHB Probability of Tenured Faculty on Committee

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The discussion centers on calculating the probabilities related to the selection of a committee from a computer systems department with eight faculty members, six of whom are tenured. The first part involves determining the probability that all three selected committee members are tenured. The second part requires calculating the probability that at least one member is not tenured, utilizing the complement rule for this calculation. The scenario is framed within a Binomial Distribution context, as each selection is a binary outcome based on tenure status. Understanding these probabilities is crucial for assessing the composition of the committee.
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"The computer systems department has eight faculty, six of whom are tenured. Dr. Vonder, the chairman, wants to establish a committee of three department faculty members to review the cur- riculum. If she selects the committee at random:
a. What is the probability all members of the committee are tenured?
b. What is the probability that at least one member is not tenured? (Hint: For this question, use the complement rule.)"
 
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trastic said:
"The computer systems department has eight faculty, six of whom are tenured. Dr. Vonder, the chairman, wants to establish a committee of three department faculty members to review the cur- riculum. If she selects the committee at random:
a. What is the probability all members of the committee are tenured?
b. What is the probability that at least one member is not tenured? (Hint: For this question, use the complement rule.)"

Since in each trial (picking a faculty member) all they are checking is whether or not the member has tenure (i.e. 2 possibilities - success or fail) this is a Binomial Distribution...
 
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