Question

In a class of 15 students, 4 failed in English, 6 failed in Mathematics and 3 failed in both. How many passed in both the subjects?

• A. 1
• B. 0
• C. 8
• D. 7

Answer 1

Answer:

C. 8

8 students passed in both subjects.

This problem can be easily solved using a Venn diagram or the set theory formula:

$n(A \cup B) = n(A) + n(B) - n(A \cap B)$

1. Find the number of students who failed at least one subject:

   • Failed English ($n(E)$) = 4

   • Failed Mathematics ($n(M)$) = 6

   • Failed both ($n(E \cap M)$) = 3

   • Total unique students who failed = $4 + 6 - 3 =$ 7 students

2. Find the number of students who passed both subjects:

   • Subtract the total number of failing students from the entire class size.

   • Passed both = $\text{Total Students} - \text{Total Failed} = 15 - 7 =$ 8 students