The records of Midwestern university show that in one semester, 38% of the students failed mathematics, 27% of the students failed physics, and 9% of the students failed both math and physics.

If a student fails physics, the probability that he failed mathematics is 9/27 = 1/3

If a student...

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The records of Midwestern university show that in one semester, 38% of the students failed mathematics, 27% of the students failed physics, and 9% of the students failed both math and physics.

If a student fails physics, the probability that he failed mathematics is 9/27 = 1/3

If a student fails mathematics the probability that he failed physics is 9/38.

The probability that a student fails both in math as well as physics is 9%.