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{"ops":[{"insert":"Suppose that I have four fair coins with values 1"},{"attributes":{"italic":true},"insert":"p"},{"insert":", 2"},{"attributes":{"italic":true},"insert":"p"},{"insert":", 5"},{"attributes":{"italic":true},"insert":"p"},{"insert":" and 10"},{"attributes":{"italic":true},"insert":"p"},{"insert":". Call the 1"},{"attributes":{"italic":true},"insert":"p"},{"insert":" coin and the 2"},{"attributes":{"italic":true},"insert":"p"},{"insert":" coin \u201clow-value\u201d coins and the other two coins \u201chigh-value\u201d coins. \n(a) What is the probability that, when I flip the coins, the 1"},{"attributes":{"italic":true},"insert":"p"},{"insert":" and the 5"},{"attributes":{"italic":true},"insert":"p"},{"insert":" come up heads, and the other two coins come up tails? To answer the question, first define the probability space (S, P). \n(b) What is the probability that at least one of the low-value coins comes up tails? \n(c) What is the probability that at least three of the coins come up tails? \n(d) What is the probability that at least three of the coins come up tails, conditioned on the fact that at least one of the low-value coins comes up tails? \n(e) Is the event that at least three of the coins come up tails independent of the event that at least one of the low-value coins comes up tails?\n"}]}
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