the venn diagram shows the number of students in an eighth - grade class taking art and drama as their…

the venn diagram shows the number of students in an eighth - grade class taking art and drama as their electives. what is the probability of a student chosen at random taking either of these subjects as an elective? 8th grade art 34 14 drama 44 15 a. $\frac{78}{107}$ b. $\frac{92}{107}$ c. $\frac{15}{107}$ d. $\frac{14}{107}$

the venn diagram shows the number of students in an eighth - grade class taking art and drama as their electives. what is the probability of a student chosen at random taking either of these subjects as an elective? 8th grade art 34 14 drama 44 15 a. $\frac{78}{107}$ b. $\frac{92}{107}$ c. $\frac{15}{107}$ d. $\frac{14}{107}$

Answer

Explanation:

Step1: Calculate total number of students

The total number of students in the class is the sum of students in art only, drama only, both art and drama, and neither. So $34 + 14+44 + 15=107$.

Step2: Calculate number of students taking either subject

The number of students taking either art or drama is the sum of students in art only, drama only, and both. So $34+14 + 44=92$.

Step3: Calculate the probability

The probability $P$ of a student taking either subject is the number of students taking either subject divided by the total number of students. So $P=\frac{92}{107}$.

Answer:

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