Questions: 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 a number from 2 to 5. Event B: The marble selected has an even number. 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 B:

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 a number from 2 to 5. Event B: The marble selected has an even number. 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 B:
Transcript text: 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 a number from 2 to 5 . Event $B$ : The marble selected has an even number. 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 $B$ ": $\square$ (b) Event " $A$ or $B$ ": $\square$ (c) The complement of the event $B$ : $\square$
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Solution

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Solution Steps

Step 1: Identify elements that satisfy both A and B (Intersection)

Given the conditions for A: 2 <= x <= 5 and B: x % 2 == 0, the outcomes that satisfy both A and B simultaneously are: ${2, 4}$.

Step 2: Identify elements that satisfy either A or B (Union)

Given the conditions for A: 2 <= x <= 5 and B: x % 2 == 0, the outcomes that satisfy either A or B (or both) are: ${2, 3, 4, 5, 6, 8}$.

Step 3: Identify elements that do not satisfy the condition for A (Complement of A)

Given the condition for A: 2 <= x <= 5, the outcomes that do not satisfy event A are: ${8, 1, 6, 7}$.

Final Answer:

(a) $A \cap B$: {2, 4} (b) $A \cup B$: {2, 3, 4, 5, 6, 8} (c) $\overline{A}$: {8, 1, 6, 7}

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