Question

select the correct answer.
the venn diagram shows the number of students in an eighth - grade class taking art and drama as their electives. fifteen of the students take neither elective.
what is the probability of a student chosen at random from the class taking either of these subjects as an elective?
8th grade
art: 34, overlap: 14, drama: 44, neither: 15
a. \\(\frac{92}{107}\\)
b. \\(\frac{15}{107}\\)
c. \\(\frac{14}{107}\\)
d. \\(\frac{78}{107}\\)

Explanation:

Step1: Calculate total elective students

$34 + 14 + 44 = 92$

Step2: Calculate total class size

$92 + 15 = 107$

Step3: Find probability of taking either elective

$\text{Probability} = \frac{\text{Students in either elective}}{\text{Total students}}$
$\text{Probability} = \frac{92}{107}$

Answer:

A. $\frac{92}{107}$