Students in a middle school must choose to take either band or chorus. in a given academic year, 60% of the pupils choose band and the rest choose chorus. 30% of the students who are taking band are girls, and 70% who are taking chorus are girls. if a student is randomly selected from this academic year, what is the probability that it is a boy?

a. 0.46

b. 0.49

c. 0.50

d. 0.54

Question

Mathematics

Lina Gordon

4 November, 13:57

Students in a middle school must choose to take either band or chorus. in a given academic year, 60% of the pupils choose band and the rest choose chorus. 30% of the students who are taking band are girls, and 70% who are taking chorus are girls. if a student is randomly selected from this academic year, what is the probability that it is a boy?

a. 0.46

b. 0.49

c. 0.50

d. 0.54

+3

Answers (1)

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Reynaldo Schneider · Answer 1

60% choose band ... 40% choose chorus

30% who are taking band are girls ... 30% of 60% is (0.3 * 0.6) = 0.18 or 18% ... so 18% are girls.

70% who take chorus are girls ... 70% of 40% is (0.7 * 0.4) = 0.28 or 28% ... so 28% are girls.

18% + 28% = 46% ... so a total of 46% taking band and chorus are girls ... so that leaves (100% - 46%) = 54% (or 0.54) are boys