Two events E1 and E2 are called independent if p(E1 E2) = p(E1)p(E2). For each of...

 

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Two events E1 and E2 are called independent if p(E1 E2) = p(E1)p(E2). For each of the following pairs of events, which are subsets of the set of all possible outcomes when a coin is tossed three times, determine whether or not they are independent. a) E1: tails come up with the coin is tossed the first time; E2: heads come up when the coin is tossed the second time. b) E1: the first coin comes up tails; E2: two, and not three, heads come up in a row. c) E1: the second coin comes up tails: E2: two, and not three, heads come up in a row. Two events E1 and E2 are called independent if p(E1 E2) = p(E1)p(E2). For each of the following pairs of events, which are subsets of the set of all possible outcomes when a coin is tossed three times, determine whether or not they are independent. a) E1: tails come up with the coin is tossed the first time; E2: heads come up when the coin is tossed the second time. b) E1: the first coin comes up tails; E2: two, and not three, heads come up in a row. c) E1: the second coin comes up tails: E2: two, and not three, heads come up in a row.