In a math class with 19 students, a test was given the same day that an assignment was due. There were 12 students who passed the test and 13 students who completed the assignment. There were 4 students who failed the test and also did not complete the assignment. What is the probability that a student completed the homework given that they passed the test?

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Accepted Answer

Step:1 ：( P(T) = frac{12}{19} )Step:2 ：( P(A cap T) = frac{12 + 13 - 19 + 4}{19} = frac{10}{19} )Step:3 ：( P(A|T) = frac{P(A cap T)}{P(T)} = frac{10/19}{12/19} )

Answer

Step: 1 ：( P(T) = frac{12}{19} )Step: 2 ：( P(A cap T) = frac{12 + 13 - 19 + 4}{19} = frac{10}{19} )Step: 3 ：( P(A|T) = frac{P(A cap T)}{P(T)} = frac{10/19}{12/19} )

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