The Schulich Society for Anarchy, Collectivism and Economic Equality has only 12 members, with surnames:
Adams, Bezos, Chung, Dirar, Efrim, Faruk, Gomes, Habib, Ikeda, Jones, Kenny, and Laval
Probably the only orderly aspect of this motley crew is the fact that there names have initials that are the first 12 letters of the alphabet. The Society does not believe in elections because they see them as competitive and destructive to the human psyche. Therefore, the Society plans to select it’s executive by random selection. However, a ferocious debate has broken out over the selection procedure to be used. The Society has also not determined whether the executive committee will be 4 or 5 members.
(a) Proposal 1, Part 1 is to form the executive committee by random selection.
i) Assuming that the executive committee is 4 people:
B) What is the probability that the executive committee has alphabetically consecutive surnames?
To calculate the probability of the executive committee having alphabetically consecutive surnames, we need to determine the number of favorable outcomes (executive committees with alphabetically consecutive surnames) and the total number of possible outcomes (all possible executive committees).
In this case, we have 12 members with surnames that follow the first 12 letters of the alphabet. We want to select a committee of 4 members.
To calculate the number of favorable outcomes, we need to consider the possible arrangements where the surnames are alphabetically consecutive.
Let's examine the possible combinations:
1. Adams, Bezos, Chung, Dirar
2. Bezos, Chung, Dirar, Efrim
3. Chung, Dirar, Efrim, Faruk
4. Dirar, Efrim, Faruk, Gomes
5. Efrim, Faruk, Gomes, Habib
6. Faruk, Gomes, Habib, Ikeda
7. Gomes, Habib, Ikeda, Jones
8. Habib, Ikeda, Jones, Kenny
9. Ikeda, Jones, Kenny, Laval
So, there are 9 favorable outcomes.
To calculate the total number of possible outcomes, we need to consider the number of ways to choose 4 members from 12. This can be calculated using the combination formula:
C(12, 4) = 12! / (4! * (12-4)!) = 495
Therefore, there are 495 total possible outcomes.
The probability of the executive committee having alphabetically consecutive surnames, assuming it consists of 4 members, is given by:
Probability = favorable outcomes / total outcomes = 9/495 = 3/165 ≈ 0.0182 or 1.82%.
So, the probability that the executive committee has alphabetically consecutive surnames under Proposal 1, Part 1, if the committee is 4 people, is approximately 0.0182 or 1.82%.