Exercise 11-10: C Assignments 11-10, 11-11 rcise 11-10: Committee A college prof

Question

Exercise 11-10: C Assignments 11-10, 11-11 rcise 11-10: Committee A college professor was assigned to a committee of six people, composed of four men and two women The committee selected two officers to carry out the majority of its administrative work, and both of the women were selected. The professor wondered whether or not this constituted evidence of subtle discrimination, so she considered how unlikely such an event would be if the two officers had been chosen at random from the six committee members.

Explanation / Answer

Let us number the possible workers as A, B, C, D, E and F. Let A and B are women out of the 6.

Thus,

Possible pairs : (AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF) = 15 pairs

Thus, only one pair contains both the women together.

Thus, theoretical probability = 1 / 15 = 6.667%

The event is very rare.

In long run, P ( 2 men) = 4C2 / 6C2

= 6/15

= 40 %

In long run, P ( 1 man, 1 woman) = 4C1 * 2C1 / 6C2

= 8/15

= 53.33 %

Thus, if two officers are chosen at random, it is mostly likely to be both males.

Theoretical expected number of males in choosing two

= 1(6/15) + 2(8/15)

= 1.46667

Hope this helps.

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