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Question 2 (40%) Consider the following random experiment: from a collection consisting of 2 humanity books, 3 social science books, and 4 natural science books

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Question 2 (40%) Consider the following random experiment: from a collection consisting of 2 humanity books, 3 social science books, and 4 natural science books (9 books in total, so no book belongs to more than one category), randomly pick 3 books with replacement. i. What is the probability of picking 3 humanity books? What is the probability of picking 3 social science books? ii. What is the probability of picking 2 humanity books, given that the rst book being picked is a humanity book? What is the probability of picking 2 humanity books, given that the humanity books have at least been picked once? Now consider the following random experiment: from a collection consisting of 2 humanity books, 3 social science books, and 4 natural science books (9 books in total, so no book belongs to more than one category), randomly pick 3 books without replacement. iii. What is the probability of picking 3 humanity books? What is the probability of picking 3 social science books? iv. What is the probability of picking 2 humanity books, given that the rst book being picked is a humanity book? What is the probability of picking 2 humanity books, given that the humanity books have at least been picked once

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