A marble is selected from a bag containing eight marbles numbered 1 to 8 . The number on the marble selected will be recorded as the outcome. Consider the following events. Event \( A: \) The marble selected has an odd number. Event \( B \) : The marble selected has a number from 3 to 6 . 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 " \( A \) and \( B \) ": \{[\} (b) Event " \( A \) or \( B \) ": \( \{[ \} \) (c) The complement of the event \( A:\{\square\} \)

Let's break this down step by step! (a) Event " \( A \) and \( B \) ": \( \{3, 5\} \) This event involves selecting a marble that is both odd (Event A) and falls between the numbers 3 and 6 (Event B). The only numbers that satisfy both conditions are 3 and 5. (b) Event " \( A \) or \( B \) ": \( \{1, 3, 4, 5, 6, 7\} \) For this event, we're looking for marbles that are either odd (1, 3, 5, 7) or fall in the range from 3 to 6 (3, 4, 5, 6). Combining these sets, we have 1, 3, 4, 5, 6, and 7. (c) The complement of the event \( A:\{2, 4, 6, 8\} \) The complement of Event A (marbles with odd numbers) includes all the numbers that are not odd. Therefore, the complement consists of the even numbers: 2, 4, 6, and 8.