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Conditional Probabilityhard
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In a clinical study, 20%20\%20% of patients take Drug X, 30%30\%30% take Drug Y, and 50%50\%50% take a Placebo. The probability of an adverse reaction for X, Y, and Placebo is 5%,8%,5\%, 8\%,5%,8%, and 2%2\%2% respectively. If a patient is known to have had an adverse reaction, what is the probability they were taking Drug Y?