In a group of 21 students, 8 students take Art courses, 7 students take Music courses. Two students take both courses. A student is chosen randomly from this group. What is the probability that the student takes either Art or Music courses?5/78/2113/212/7

Answer:13/21Step-by-step explanation:Givens:There are 21 students in total.8 students take Art,7 students take Music.2 students take both.So, in the problem, we have two sets labeled as Art and Music, and an intersection between these two sets.To answer the question we have to consider that it's asking about a probability of one or another, when that happens, we actually need to find the probability of the union of both sets, which is defined as:[tex]P(AorB)=P(A)+P(B)-P(A andB)[/tex]This means that the probability of students that takes either Art or Music, refers only to those that only are in those courses, not in the intersection, that's why it has to be subtracted:[tex]P(AorB)=\frac{8}{21}+\frac{7}{21}-\frac{2}{21}=\frac{13}{21}[/tex]Therefore, the right answer is 13\21.Remember that the probability including "or", refer to the probability of the union of sets, from which must be subtract the intersection.