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In a math class with 22 students, a test was given the same day that an assignmentwas due. There were 14 students who passed the test and 13 students who completedthe assignment. There were 6 students who failed the test and also did not completethe assignment. What is the probability that a student chosen randomly from theclass passed the test and completed the homework?



Answer :

Let:

A = students who passed the test = 14

B = students who completed the assignment = 13

N = Total students = 22

(A⁺ ∩ B⁺) = 6

P(A ∪ B) = 1 - 6/22 = 8/11

P(A ∩ B) = P(A) + P(B) - P(A ∪ B) = 14/22 + 13/22 - 8/11 = 1/2

P(A|B) = P(A ∩ B)/P(B) = (1/2)/(13/22) = 11/13 ≈ 0.85 ≈ 85%

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