Exercise 1110 Committee Assignments 1110 1111 A college prof

Exercise 11-10: Committee Assignments 11-10, 11-11 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.

Solution

Choosing two women from a group of 6 would have a probability

= ²C₂ / ⁶C₂

= 1 /15

a)

Let us assign a number from 1 to 6 to each member of the group.

Thus, A-1, B-2, C-3, D-4, E-5 and F-6

Then, the dice can be rolled twice to determine the two people on the committee. If the same number turns up, we must roll again.

A and B are females. The iterations are:

Over here, 6 times out of 50, the two women have ended up together = 6 / 50 = 12% (empirically)

which is twice the expected probability.

Mean number of men in the stimulated pairs = 67 men in 100 samples

Hope this helps.

simulation	Roll 1	Roll 2
1	6	2
2	5	4
3	4	1
4	4	3
5	6	3
6	1	2
7	5	2
8	6	5
9	4	5
10	2	4
11	4	6
12	6	2
13	3	4
14	6	5
15	2	1
16	4	5
17	3	4
18	5	4
19	4	6
20	4	2
21	6	3
22	2	3
23	1	2
24	6	4
25	5	1
26	5	4
27	1	2
28	5	3
29	1	6
30	4	6
31	1	6
32	2	6
33	2	4
34	6	1
35	1	6
36	2	1
37	5	3
38	4	3
39	4	5
40	1	4
41	6	1
42	5	6
43	4	1
44	1	4
45	3	4
46	1	6
47	2	1
48	4	2
49	6	3
50	1	3