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 an even 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 or B": (b) Event "A and 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 an even 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 or B": (b) Event "A and 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 an even 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 " $A$ or $B$ ": $\square$ (b) Event " $A$ and $B$ ": $\square$ (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: x % 2 == 0 and B: 3 <= x <= 6, the outcomes that satisfy both A and B simultaneously are: ${4, 6}$.

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

Given the conditions for A: x % 2 == 0 and B: 3 <= x <= 6, 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: x % 2 == 0, the outcomes that do not satisfy event A are: ${1, 3, 5, 7}$.

Final Answer:

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

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