1. A student has to take a midterm exam and a final exam for a course....

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1. A student has to take a midterm exam and a final exam for a course. He has to pass at least one of the two exams to pass the course. Suppose that the probability of him passing the first exam is p € (0,1) the probability of passing both exams is also p; the probability of failing the first one but passing the second one is p/2. (hint: just keep p as a parameter in your calculations) (a) What's the probability of this student passing the course? (b) If we know that this student passed the second exam, what's the probability of he passing the first exam? 2. Suppose that A and B are two events such that A'nB = An B'. Verify that P(A|B) = P(BA). 3. Suppose that A and B are two events such that P(A/B) = 1. Calculate P(B'|A'). 1. A student has to take a midterm exam and a final exam for a course. He has to pass at least one of the two exams to pass the course. Suppose that the probability of him passing the first exam is p € (0,1) the probability of passing both exams is also p; the probability of failing the first one but passing the second one is p/2. (hint: just keep p as a parameter in your calculations) (a) What's the probability of this student passing the course? (b) If we know that this student passed the second exam, what's the probability of he passing the first exam? 2. Suppose that A and B are two events such that A'nB = An B'. Verify that P(A|B) = P(BA). 3. Suppose that A and B are two events such that P(A/B) = 1. Calculate P(B'|A').

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