Exercise 188 Page 664

a We have been given the number of freshmen, sophomores, and juniors at the school. If we subtract the number of students in these age ranges from 27 000 we can determine the number of seniors at the school.

27 000-7776-6750-6750=5724

The exercise states that 18 % of the students in any particular class are in the performing arts. If we multiply the number of seniors by 0.18, we can determine the number of seniors in the performing arts. (0.18)(5724)≈ 1030 people When we know the number of people in the performing arts that are seniors, we can calculate the probability of a senior being in the performing arts. P(Seniors in performing arts)=1030/27 000≈ 3.8 %

b From the exercise, we know that about 18 % of all students in each class are in the performing arts. This must mean that class does not affect the number of students in the performing arts. Therefore, they are independent.

c To determine the probability that someone in the performing arts is a senior, we have to know how many students are in the performing arts. From Part A, we know that 1030 seniors are in the performing arts. From the exercise, we know that 18 % of all classes are in the performing arts. We can find the number of students in the performing arts in each class.

P(Freshman) &= (0.18)(7776)=1400 P(Juniors) &= (0.18)(6750)=1215 P(Sophmores) &= (0.18)(6750)=1215

With this information we can find the total number of students in the performing arts. 1030+1400+1215+1215=4860 When we know the number of students in the performing arts we can determine the probability of being a senior if the student is in the performing arts. P(Senior|performing arts)=1030/4860≈ 21.2 %

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Exercise 188 Page 664

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