04spex1 - Math 431 First Evening Exam Room B239 6:15 7:15pm...

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Unformatted text preview: Math 431 First Evening Exam Room B239, 6:15 - 7:15pm, February 23, 2004 M´arton Bal´azs NAME: 1. The 35 different symbols and letters of the Braille alphabet are encoded by the presence or lack of points at the following six positions: ◦ ◦ ◦ ◦ ◦ ◦ An example of a five letter word: • • ◦ ◦ • ◦ h • ◦ ◦ ◦ • ◦ e • • • ◦ ◦ ◦ l • • • ◦ ◦ ◦ l • ◦ • ◦ • ◦ o (a) (20 points) We flip a fair coin for each of the six points and make it present or not present in case of heads or tails, respectively. What is the probability that the resulting configuration is actually a Braille-character? (b) (20 points) Five out of the 35 encoded characters consist of two points, like the letter “e” above. What is the probability that the resulting configuration is a Braille-character, given that the number of points present in it is two? (c) (10 points) Which of the answers for (a) and (b) could change in case of a biased coin? Is it possible to tell how it changes then?...
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04spex1 - Math 431 First Evening Exam Room B239 6:15 7:15pm...

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