Part I: Probability For each of the following problems, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. 5. 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. Calculate the probability of each event; that is, p(M), p(T), and p(S). 5.1 5.2 What is p(MIT)? 5.3 What is p(MIS)? 5.4 5.5 What is p(T|S)? 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.
Part I: Probability For each of the following problems, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. 5. 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. Calculate the probability of each event; that is, p(M), p(T), and p(S). 5.1 5.2 What is p(MIT)? 5.3 What is p(MIS)? 5.4 5.5 What is p(T|S)? 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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Part I: Probability
For each of the following problems, you should write your answer as an expression. Do not
give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375.
5.
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.
Calculate the probability of each event; that is, p(M), p(T), and p(S).
5.1
5.2
What is p(MIT)?
5.3
What is p(MIS)?
5.4
5.5
What is p(T|S)?
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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