Question

#3. In the freshmen class, 62% of the students take Math, 49% take Science, and 38% take both Science and Math. What percentage take at least one Science or Math course?

Answer 1

Let A be the event that a student takes math, B be the event that a student takes science. Then we are given that

P(A) = 62% =0.62 , P(B) = 49% =0.49 and P(A$\bigcap$ B ) = 0.38 . We have to calculate the percentage of students that take at least one science or math course. In probability theory, at least one is given by A$\bigcup$B. Hence we have to calculate P(A$\bigcup$B). Using probability formula of set theory P(A$\bigcup$B) is given by

P(A$\bigcup$B) = P(A) + P(B) - P(A$\bigcap$ B ) = 0.62+0.49 -0.38 = 0.73

Hence 73% students take at least one science or math course.