Law of total probabilities Archie is taking a course in probability theory. Discussion sessions with the class TA (teaching assistant) conflict with Archie's trips to the beach. Archie has to decide between attending TA sessions, which might help him do better in the probability course, and going to the beach. Archie learns that % of past students who did not attend TA sessions received a grade of B or below in the course. Archie also learns that % of past students received a grade higher than B. After some thought, Archie decides to attend the TA sessions. Not all of his classmates share his decision; in fact, only out of every of his classmates attend discussion sessions with the TA. Compute the probability that Archie will receive a grade higher than a B in the course. Round your answer to two decimal places. (If necessary, consult a list of formulas .) We'll examine the information in the above paragraph. We'll write for the event "achieves a grade higher than a B." We are told that the probability of this event is . We'll write for the event "meets in discussion sessions with the TA," and we'll write for the complementary event. We are told that
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