Which of the following represents the sample space for the event of selecting a vowel at random from the alphabet A a b c d e f g h i j k l m n o p q r s t u v w x y z B b c d f g h j k l m n p q r s...

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Which of the following represents the sample space for the event of selecting a vowel at random from the alphabet? (A) $\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}, \mathrm{g}, \mathrm{h}, \mathrm{i}, \mathrm{j}, \mathrm{k}, \mathrm{l}, \mathrm{m}, \mathrm{n}, \mathrm{o}, \mathrm{p}, \mathrm{q}, \mathrm{r}, \mathrm{s}, \mathrm{t}, \mathrm{u}, \mathrm{v}, \mathrm{w}, \mathrm{x}, \mathrm{y}, \mathrm{z}\}$ (B) $\{\mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{f}, \mathrm{g}, \mathrm{h}, \mathrm{j}, \mathrm{k}, \mathrm{l}, \mathrm{m}, \mathrm{n}, \mathrm{p}, \mathrm{q}, \mathrm{r}, \mathrm{s}, \mathrm{t}, \mathrm{v}, \mathrm{w}, \mathrm{x}, \mathrm{y}, \mathrm{z}\}$ (C) $\{\mathrm{a}, \mathrm{e}, \mathrm{i}, \mathrm{o}, \mathrm{u}\}$ (D) $\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}\}$

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#### Solution By Steps ***Step 1: Identify Vowels*** Vowels in the English alphabet are $\{\mathrm{a}, \mathrm{e}, \mathrm{i}, \mathrm{o}, \mathrm{u}\}$. ***Step 2: Sample Space*** The sample space for selecting a vowel at random is the set of vowels: $\{\mathrm{a}, \mathrm{e}, \mathrm{i}, \mathrm{o}, \mathrm{u}\}$. #### Final Answer (C) $\{\mathrm{a}, \mathrm{e}, \mathrm{i}, \mathrm{o}, \mathrm{u}\}$ #### Key Concept Sample Space #### Key Concept Explanation The sample space represents all possible outcomes of an experiment. In this case, the sample space for selecting a vowel from the alphabet consists of the vowels $\{\mathrm{a}, \mathrm{e}, \mathrm{i}, \mathrm{o}, \mathrm{u}\}$.

Follow-up Knowledge or Question

What is the definition of a sample space in probability theory?

What is the difference between an event and a sample space in probability theory?

Can you provide an example of a sample space for a different probability experiment?

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