2. Provide a representation of the sample space for each of the following experiments. Suppose that a box contains 5 balls numbered from 1 to 5. Suppose further that the balls numbered 1, 2 are red while the balls numbered 3, 4, and 5 are green. (a) Three balls are selected at random with replacement from the balls in the box described above. (b) Three balls are selected at random without replacement from the balls in the box described above. (c) Four balls are selected at random with replacement from the balls in the box described above and the number of red balls in the selection is recorded. (d) Four balls are selected at random without replacement from the balls in the box described above and the number of red balls in the selection is recorded.
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The sample space can be represented as the set of all possible 3-tuples, where each element can be a number from 1 to 5. $$\boldsymbol{S_a = \{(i, j, k) \mid i, j, k \in \{1, 2, 3, 4, 5\}\}}$$ Show more…
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