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