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Suppose a researcher is conducting a randomized experiment to compare a herbal remedy and placebo for treating common cold. The response variable are the cold's severity and duration. There are 4 volunteers, two men (Anuj and Rishi) and two women (Swati and Prabha). Two of these volunteers will be randomly chosen to receive the herbal remedy and the rest two will receive the placebo.
Q1. Identify the possible samples to receive the herbal remedy. This is the sample space for randomly choosing 2 out of 4 people.
Q2. For each possible sample, what is the probability that it is chosen ? Since each possible sample is equally likely, each of them has probability of of being chosen. Clearly the total probability of the sample space is
Q3. What is the probability of the event that a man-woman pair will receive the herbal remedy ? The event in which a man-woman pair will be selected consists of the outcomes Since each outcome has probability , the probability of this event is.
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