A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. The letter selected will be recorded as the outcome. Consider the following events. Event \( X \) : The letter selected comes before " \( D \) ". Event \( Y \) : The letter selected is found in the word "CAGE". Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas. (a) Event " \( X \) or \( Y \) ": \{in

To determine the outcomes for the event " \( X \) or \( Y \) ", let's first identify the individual events: - **Event \( X \):** The letter selected comes before " \( D \) " in the alphabet. - Letters before D: **A**, **B**, **C** - **Event \( Y \):** The letter selected is found in the word "CAGE". - Letters in "CAGE": **C**, **A**, **G**, **E** **Event " \( X \) or \( Y \) ":** This includes any letter that is either in Event \( X \) or Event \( Y \) (or both). Combining the outcomes: - From \( X \): **A**, **B**, **C** - From \( Y \): **C**, **A**, **G**, **E** The union of these sets is: **A**, **B**, **C**, **E**, **G** **Answer:** (a) Event " \( X \) or \( Y \) ": {A, B, C, E, G}