Question

In a group of 15,7 have studied Latin, 8 have studied Greek, and 3 have not studied either.How many of these studied both Latin and Greek

A.0 B.3 C.4 D.5

Answer 1

Answer:ans = option B (3)

Step-by-step explanation:

p(A U  B) = p(A)+ p(B)- P(A∩B)

here  P(A∩B)  here  its  means  both  students  studied  in latin and geeks .

p(AUB) is  total  group members

then

15=8+7-P(A∩B)

P(A∩B)=3

Answer 2

Given:

In a group of 15 students,

7 have studied Latin,

8 have studied Greek,

3 have not studied either.

To find:

The number of students who studied both Latin and Greek.

Solution:

In a group of 15 students, have studied Latin, 8 have studied Greek, 3 have not studied either.

Therefore,

n(A∪B) = 15 - 3

n(A∪B) = 12

7 have studied Latin,

n(A) = 7

8 have studied Greek,

n(B) = 8

n(A∩B) is the number of students who studied both Latin and Greek.

n(A∩B) = n(A) + n(B) - n(A∪B)

n(A∩B) = 7 + 8 - 12

n(A∩B) = 15 - 12

n(A∩B) = 3

The number of students who studied both Latin and Greek is 3

Final answer:

3 of them studied both Latin and Greek.

Thus, the correct option is B.3