Question

Affirmative action commitments by many organizations have led to an increase in the number of women in executive positions. Satellite Office Systems has vacancies for two executives that it will fill from among four women and six men. What is the probability that no woman is selected

Answer 1

Answer:

0.3333 = 33.33%

Step-by-step explanation:

We have 2 vacancies that will be filled from among 10 people, so the number of combinations we have is a combination of 10 choose 2, which is 10*9/2 = 45 possibilities.

Among these possibilities, the cases where the 2 vacancies are occupied by men is:

We have 6 men for 2 vacancies, so is a combination of 6 choose 2, which is 6*5/2 = 15 cases.

From the 45 cases we have, 15 are cases that no woman was selected, so the probability that no woman is selected is 15/45 = 1/3 = 0.3333 = 33.33%

Answer 2

Answer:

The probability that no woman is selected is 1/3 or 0.33

Step-by-step explanation:

Now, before proceeding, it is necessary to firstly determine the Probability of selecting a single woman and the probability of selecting one man.

In the question, we were told that the vacancies for the two executives must be filled from a committee of four women and six men. This means that the total number of people from which the two executives are to be chosen or selected from is ten (10).

Then the probability of picking one man out of the group of of four women and six men is = the number of men/total number of people in the group = 6/10

Similarly, the probability of picking or selecting a woman out of the entire group =

the number of women in the group/total number of people therein = 4/10

The probability that a woman will not be selected is then =

The probability that two men will be selected to fill up the vacancies (This selection is without replacement).

P(selecting two men) =

6/10 × 5/9

= 30/90

= 1/3 or 0.33