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
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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.
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.
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