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Unformatted text preview: E 1 E 2 ) = P ( E 1 ) P ( E 2 ) = 1 12 and thus they are independent. 3. (4 pts) Suppose you ip a biasp coin four times and it comes up heads exactly twice. Whats the probability that the second ip was a tails? Recall that a biasp coin is one that comes up heads with probability p . Let E be the event It comes up head exactly twice and F be the event the second is a Tails. So we want P ( F  E ) = P ( E F ) P ( E ) By Bernoulli, P ( E ) = ( 4 2 ) p 2 (1p ) 2 . E F = { HTHT,HTTH,TTHH } . Each outcome here has probability p 2 (1p ) 2 so P ( E F ) = 3 p 2 (1p 2 ) and we have P ( F  E ) = 3 p 2 (1p ) 2 6 p 2 (1p ) 2 = 1 2...
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 Summer '08
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 Math, Probability

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