The qualified applicant pool for six management trainee positions consist of sev
ID: 3314576 • Letter: T
Question
The qualified applicant pool for six management trainee positions consist of seven women and five men. Assuming that the applicants are equally qualified and the trainee positions are selected at random, calculate the following probabilities. Enter the answer in percent notation rounded to the nearest hundredth (a value at hundredth position must be shown).
a) What is the probability that the trainee group will consist entirely of women?
b) What is the probability that the trainee group will consist entirely of men?
c) What is the probability that the trainee group will consist of three men and three women?
d) What is the probability that the trainee group will consist of more than four women?
Explanation / Answer
There are 7 women and 5 men, 12 people in total. The trainee group consists of 6 people.
In all, we can choose the group in 12C6 = 12! / (6! * 6!) = 924 ways.
a) We can choose all 6 women trainees out of 7 in 7C6 = 7 ways.
The probability is 7/924 = 0.01.
b) There are six members in the group but there are only five men. A group cannot be formed with only men.
Therefore, the probability that the trainee group will consist entirely of men = 0.00.
c) The three men can be selected out of five in 5C3 = 5 * 4 / 2 = 10 ways.
The three women can be selected out of seven in 7C3 = 7 * 6 * 5 / 6 = 35 ways.
The six people can be chosen in 10 * 35 = 350 ways.
Probability = 10 / 924 = 0.01.
d) If five women are to be selected, we can choose them out of 7 in 7C4 = (7 * 6 * 5) / (3 * 2 * 1) = 35 ways.
The one man can be chosen out of 5 in 5 ways.
Therefore, we can choose one man and five women in 35 * 5 = 175 ways.
The probability is 175/924.
Therefore, the probability of choosing more than 4 women = 175/924 + 7 / 924 = 182 / 924 = 0.20.
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