The gender and year of each of the 191 students in a high school band were recorded. The data are summarized in the table below.Freshman Sophomore Junior SeniorMale 30 14 21 18Female 42 22 17 27Suppose a student from the high school band is chosen at random.Answer each part. Do not round intermediate computations, and round your answers to the nearest hundredth.(If necessary, consult a list of formulas.)(a) What is the probability that the student is female or a freshman?(b) What is the probability that the student is male, given that the student is a sophomore?
Question
The gender and year of each of the 191 students in a high school band were recorded. The data are summarized in the table below.Freshman Sophomore Junior SeniorMale 30 14 21 18Female 42 22 17 27Suppose a student from the high school band is chosen at random.Answer each part. Do not round intermediate computations, and round your answers to the nearest hundredth.(If necessary, consult a list of formulas.)(a) What is the probability that the student is female or a freshman?(b) What is the probability that the student is male, given that the student is a sophomore?
Solution
(a) To find the probability that the student is female or a freshman, we first need to find the total number of female students and the total number of freshman students.
From the table, we can see that there are 42 + 22 + 17 + 27 = 108 female students and 30 + 42 = 72 freshman students. However, we have counted the female freshman students twice, once in the female count and once in the freshman count. There are 42 female freshman students.
So, the total number of students who are either female or freshman is 108 + 72 - 42 = 138.
The total number of students is 191.
So, the probability that the student is female or a freshman is 138 / 191 = 0.72 (rounded to the nearest hundredth).
(b) To find the probability that the student is male, given that the student is a sophomore, we first need to find the total number of male sophomores and the total number of sophomores.
From the table, we can see that there are 14 male sophomores and 14 + 22 = 36 sophomores.
So, the probability that the student is male, given that the student is a sophomore, is 14 / 36 = 0.39 (rounded to the nearest hundredth).
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