Question

a bag has nine balls labeled a, b, c, d, e, f, g, h, and i. one ball will be randomly picked, and its letter will be recorded as the outcome. give the sample space describing all possible outcomes. then give all of the outcomes for the event of choosing a vowel. if there is more than one element in the set, separate them with commas. sample space: {} event of choosing a vowel: {}

Explanation:

Step1: Determine the sample space

The sample space is the set of all possible outcomes. Since the balls are labeled \(A, B, C, D, E, F, G, H, I\), the sample space \(S=\{A,B,C,D,E,F,G,H,I\}\).

Step2: Identify vowels

In the English alphabet, vowels are \(A, E, I\). So the event of choosing a vowel \(E = \{A,E,I\}\).

Answer:

Sample space: \(A,B,C,D,E,F,G,H,I\)
Event of choosing a vowel: \(A,E,I\)