Affirmative action commitments by industrial organizations have led to an increase in the number of women in executive positions. Satellite Office Systems has vacancies for two executives, which it will fill from among four women and six men. What is the probability that two woman are selected?
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A. B. C. D. E.Explanation
Probability of both positions being filled by women = 4/10*3/9 = 12/90.
To calculate the probability that two women are selected from a group of four women and six men for the executive positions, we can use the concept of combinations.
The total number of people from which the selection is made is the sum of the number of women and the number of men: Total = 4 women + 6 men = 10 individuals
Now, we need to determine the number of ways to select two women from the group of four women. This can be calculated using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
Where C(n, r) represents the number of combinations of selecting r items from a set of n items, and "!" denotes the factorial of a number.
In this case, we want to calculate C(4, 2) because we are selecting 2 women from a group of 4 women. Plugging in the values, we get:
C(4, 2) = 4! / (2! * (4 - 2)!) = 4! / (2! * 2!) = (4 * 3 * 2!) / (2! * 2!) = (4 * 3) / 2! = 12 / 2 = 6
So, there are 6 ways to select two women from the group of four women.
Next, we need to determine the total number of ways to select two executives from the entire group of ten individuals. This can be calculated as C(10, 2):
C(10, 2) = 10! / (2! * (10 - 2)!) = 10! / (2! * 8!) = (10 * 9) / (2 * 1) = 90 / 2 = 45
Therefore, there are 45 ways to select two executives from the entire group.
To find the probability, we divide the number of favorable outcomes (i.e., selecting two women) by the total number of possible outcomes (i.e., selecting any two executives). So, the probability is:
Probability = Number of favorable outcomes / Total number of possible outcomes = 6 / 45 = 2 / 15
Therefore, the probability that two women are selected as executives is 2/15.
The correct answer is D. 2/15.