(25 pt.) You are playing Scrabble and you draw seven tiles: M, A, T, C, H, E, S. You line them up in some random order on your tile rack (assume all orderings are equally likely). The events M, T, and S are defined as follows: M: The tiles M, A, T, H appear consecutively. T: The tile T appears exactly in the middle (fourth position). S: The tile S is either in the first position or in the final position. 5.1 (9 pt.) Calculate the probability of each event; that is, p(M), p(T), and p(5). 5.2 (4 pt.) What is p(M/T)? 5.3 (4 pt.) What is p(M|5)? 5.4 (4 pt.) What is p(T|S)? 5.5 (4 pt.) Consider all pairs of events: (M,T), (M,S), and (T.S). Which pairs of events are Independent and which pairs of events are not independent? Justify your answer.
(25 pt.) You are playing Scrabble and you draw seven tiles: M, A, T, C, H, E, S. You line them up in some random order on your tile rack (assume all orderings are equally likely). The events M, T, and S are defined as follows: M: The tiles M, A, T, H appear consecutively. T: The tile T appears exactly in the middle (fourth position). S: The tile S is either in the first position or in the final position. 5.1 (9 pt.) Calculate the probability of each event; that is, p(M), p(T), and p(5). 5.2 (4 pt.) What is p(M/T)? 5.3 (4 pt.) What is p(M|5)? 5.4 (4 pt.) What is p(T|S)? 5.5 (4 pt.) Consider all pairs of events: (M,T), (M,S), and (T.S). Which pairs of events are Independent and which pairs of events are not independent? Justify your answer.
C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter4: Selection Structures
Section: Chapter Questions
Problem 14PP
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Transcribed Image Text:(25 pt.) You are playing Scrabble and you draw seven tiles: M, A, T, C, H, E, S. You line
them up in some random order on your tile rack (assume all orderings are equally likely).
The events M, T, and S are defined as follows:
M: The tiles M, A, T, H appear consecutively.
T: The tile T appears exactly in the middle (fourth position).
S: The tile S is either in the first position or in the final position.
5.1 (9 pt.) Calculate the probability of each event; that is, p(M), p(T), and p(5).
5.2 (4 pt.) What is p(M/T)?
5.3 (4 pt.) What is p(M|5)?
5.4 (4 pt.) What is p(T|S)?
5.5 (4 pt.) Consider all pairs of events: (M,T), (M,S), and (T.S). Which pairs of events are
Independent and which pairs of events are not independent? Justify your answer.
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