The dean of a business school wishes to form an executive committee of 6 from am

Question

The dean of a business school wishes to form an executive committee of 6 from among the 35 tenured faculty members at the school. The selection is to be random, and at the school there are 9 tenured faculty members in accounting. What is the probability that the committee will contain.

A. What is the probability that the committee will contain none of the tenured faculty members in accounting?

B. The probability that the committee will contain at least 1 of the tenured faculty members in accounting is the complement of the probability that the committee will contain none of them.

C. If the committee contains no more than 2 of the tenured faculty members in accounting, then it must contain 0, 1, or 2 of them.

Explanation / Answer

A. P( the committee will contain none of the tenured faculty members in accounting) = 26C6/35C6

= 230230/1623160 = 0.1418

B. P(the committee will contain at least 1 of the tenured faculty members in accounting ) = 1 - 0.1418 = 0.8581

C. P(the committee contains no more than 2 of the tenured faculty members in accounting) = P( no accounting faculty) + P( 1 accounting faculty) + P(2 accounting faculties)

= 0.1418 + 9C1*26C5/35C6 +  9C2*26C4/35C6

= 0.1418 + 9*65780/1623160 + 36*14950/1623160

= 0.1418 + 0.36473 + 0.33157

= 0.83814

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