If 75 % of a class answered the first question on a certain test correctly, 55…
2024
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?
Answer: C. 50 — Solution: Let A be the event that a student answered the first question correctly and B the event that a student answered the second question correctly. Given…
- A.
30
- B.
40
- C.
50
- D.
60
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Correct answer: C
Solution: Let A be the event that a student answered the first question correctly and B the event that a student answered the second question correctly.
Given P(A)=0.75, P(B)=0.55, and 20% answered neither, so P(A∪B)=1−0.20=0.80.
Use the formula P(A∪B)=P(A)+P(B)−P(A∩B).
Solve for P(A∩B): P(A∩B)=P(A)+P(B)−P(A∪B)=0.75+0.55−0.80=0.50, which is 50%.
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