If 75 % of a class answered the first question on a certain test correctly, 55…
2026
If 75 % of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percentage answered both correctly
- A.
40 %
- B.
50%
- C.
60 %
- D.
45 %
Attempted by 2255 students.
Show answer & explanation
Correct answer: B
Let be A be group of students who answered 1st question correctly while that
B be group of students who answered 2nd question correctly.
Assuming 100 students in the class.
Given, n(A) = 75 n(B) = 55 , n(A' ∩ B') = 20
n(A'∩B') = 100 - n(A U B) ⇒ n(A U B) = 100- 20 = 80
n(A U B) = n(A) + n(B) - n(A ∩ B) ⇒ 80= 75 + 55 - n(A ∩ B)
n(A ∩ B) = 50
Hence 50 % of students answered both questions correctly.