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Chapter 7: Problem 26

An experiment consists of selecting a letter at random from the letters in the word MASSACHUSETTS and observing the outcomes. a. What is an appropriate sample space for this experiment? b. Describe the event "the letter selected is a vowel."

Short Answer

Expert verified
a. The appropriate sample space for this experiment is \(S = \{ M, A, S, C, H, U, T, E \}\). b. The event "the letter selected is a vowel" is represented as \(V = \{ A, E, U \}\).

Step by step solution

01

Identify all distinct letters in 'MASSACHUSETTS'

To find the sample space, we need to list all the possible outcomes that can be obtained when selecting a letter randomly from the word "MASSACHUSETTS." The distinct letters are: M, A, S, C, H, U, T, and E.
02

Write down the sample space

Now that we have identified all distinct letters in the word "MASSACHUSETTS." Let's represent the sample space as a set, with each element corresponding to a distinct letter. The sample space is: \(S = \{ M, A, S, C, H, U, T, E \}\). #b. Describe the event "the letter selected is a vowel."#
03

Identify the vowels in 'MASSACHUSETTS'

To describe the event of selecting a vowel, we need to list all the vowels in the word "MASSACHUSETTS". The vowels are A, E, and U.
04

Write down the event

Now that we have identified all vowels in the word "MASSACHUSETTS," let's represent the event as a set, with each element corresponding to a vowel. The event "the letter selected is a vowel" is: \(V = \{ A, E, U \}\).

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