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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 ?
45
60
50
40
30
45
60
50
40
30
Solution
Let, the total number of students in the class = 100
Then the number of students who answered first question correctly is
= n(1) = 75
Then the number of students who answered second question correctly is
= n(2) = 55
Then the number of students who answered neither of the question correctly = 20
Then the number of students who answered at least one of the question correctly = 100 − 20 = 80
The number of students who answered both question correctly = n(1 ∩ 2)
n(1 U 2) = n(1) + n(2) − n(1 ∩ 2)
80 = 75 + 55 − n(1 ∩ 2)
Therefore, n(1 ∩ 2) = 50
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Solution
Keynote
n(a U b) = n(a) + n(b) − n(a ∩ b)
