statistical analasis

Question

The Computer Systems Department has eight faculty, six of whom are tenured. Dr. Vonder, the chair, wants to establish a committee of three department faculty members to review the curriculum. 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).

Answer 1

(a) The probability the first is tenured is 6/8; the second is 5/7; the third is 4/6.

 

Multiply these together.

 

(b) P(at least 1 not tenured)= 1 - P(all  tenured)  = 1 - answer in part (a)

 

 

Any questions comment back.

Answer 2

a.  You are selecting a 3 person committee. Since 3/4 or .75 are tenured,  the probability of of each member is .75.

So of the  three people, each has a .75 probability

The probability that all 3 are tenured is .75 x .75 x .75 or .42

 

b.  The probability that one member is not tenured is .25 (6/8). This follows the complementary rule.  The probability that all three are not tenured is:

 .25 x .25 x.25 or .015 rounded to .02