Unformatted text preview: P { N > 5 } occurred, what is the expected value of N ? (d) [10 points] Find the numerical value of E [cos( πN )]. 4. [20 points] A fair coin is tossed 10 times. Calculate the probability that the ﬁrst 5 tosses are all Tails given that a total of 8 Tails occurred on the 10 tosses. 5. [25 points] Dilbert has 3 coins in his pocket, 2 of which are fair coins while the third is a biased coin with P ( H ) = p 6 = 1 2 . The probability that a coin chosen at random from his pocket will land Tails is 7 12 . (a) [10 points] What is the value of p ? (b) [15 points] Dilbert picks two coins at random from his pocket, tosses each coin once, and observes a Head and a Tail. What is the conditional probability that both coins are fair?...
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 Spring '08
 Milenkovic,O
 Probability theory, fair coin, Noyes Laboratory

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