Question

The dean of a business school wishes to form an executive committee of 5 from among the 35 tenured faculty members at the school. The selection is to be​ random, and at the school there are 8 tenured faculty members in accounting. What is the probability that the committee will contain

a. none of​ them? b. at least 1 of​ them? c. not more than 2 of​ them?

Answer 1

Solution:
Given in the question
Total number of faculty member (N)= 35
Total number of accounting members (A)= 8
Number of draws(n) = 5
Solution(a)
No. of accounting members selected(x) = 0
Here we. will use Hypergeometric distribution
P(X=x,| n,N,A) = (ACx)*(N-A)C(n-x) / NCn = (8C0)*(35-8)C(5-0)/35C5 = 1*80730/324632 = 0.2487
So there is 24.87% probability that none of them are tenure faculty member in accounting
Solution(b)
Here need to calculate
P(X<=1) = 1- P(X=0) = 1 - 0.2487 = 0.7513
So there is 75.13% probability that there is at least 1 of them in accounting.
Solution(c)
Here we need to calculate
P(X<=2) = 1 - P(X=0) - P(X=1) - P(X2) = 1 - (8C0)*(35-8)C(5-0)/35C5 - (8C1)*(35-8)C(5-1)/35C5 - (8C2)*(35-8)C(5-2)/35C5 = 1 - 0.2487 - 0.4325 - 0.2523 = 0.0665
So there is 6.65% probability that not more than 2 of them faculty members in accounting.