What are the sample points of $$ \mathrm{A} \cup \mathrm{B} $$ if $$ \mathrm{A}=\{1,2,5,7,8\} $$ and $$ \mathrm{B}=\{2,4,6,8,9\} ? $$ a. $$ \{2,8\} $$ b. $$ \{1,2,4,5,6,7,8,9\} $$ c. $$ \{1,2,4,6,8,91 $$ d. $$ \{1,5\} $$ These events have common outcomel. a. mutually exclusive b. not matually exclusive c. complement d. internection When you draw a cand form a standard deck of cards, whar is the probability of getting a club or a red cand? a. $$ \frac{3}{4} $$ b. $$ \frac{32}{12} $$ c. $$ \frac{1}{4} $$ d. $$ \frac{13}{52} $$ Which of the following is the formula for probability of mutually exclusive events? a. $$ \mathbf{P}(A)+\mathbf{P}(B) $$ b. $$ P(A)+P(B)+P(A \cap B) \subset P(A)-P(B) $$ d. $$ P(A){ }^{*} P(B) $$ These events do not have common outcomels. a. not mutually exclusive b. complement c. mutually exclusive 4. intersection What kind of events are being illustrated if you are attending an online class or using the internet at the same time? a. mutually exclusive b. intersection c. not mutually exclusive d. complement

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1. To find $$ \mathrm{A} \cup \mathrm{B} $$, take all distinct elements from both sets.  
   - Given $$ \mathrm{A}=\{1,2,5,7,8\} $$ and $$ \mathrm{B}=\{2,4,6,8,9\} $$,  
   - The union is  
     $$
     \mathrm{A} \cup \mathrm{B}=\{1,2,4,5,6,7,8,9\}.
     $$
   - Therefore, the correct answer is **b.** $$ \{1,2,4,5,6,7,8,9\} $$.

2. If two events have common outcomes, they are said to be overlapping.  
   - When events share common outcomes, they are **not mutually exclusive**.  
   - The correct answer is **b.** not mutually exclusive.

3. When drawing a card from a standard deck:
   - A standard deck contains 52 cards.
   - The number of clubs is 13.
   - The number of red cards (hearts and diamonds) is 26.
   - Since clubs and red cards do not overlap (clubs are black), the probability of drawing a club or a red card is:
     $$
     P(\text{club or red})=\frac{13}{52}+\frac{26}{52}=\frac{39}{52}=\frac{3}{4}.
     $$
   - Therefore, the correct answer is **a.** $$ \frac{3}{4} $$.

4. For mutually exclusive events $$ A $$ and $$ B $$, we know that:
   - $$ A \cap B=\emptyset $$ so the formula for the probability of $$ A $$ or $$ B $$ is:
     $$
     P(A \text{ or } B)=P(A)+P(B).
     $$
   - Therefore, the correct answer is **a.** $$ \mathbf{P}(A)+\mathbf{P}(B) $$.

5. When two events do not have any common outcomes, they are by definition:
   - **Mutually exclusive.**
   - Therefore, the correct answer is **c.** mutually exclusive.

6. Consider the situation: attending an online class and using the internet.  
   - These events can happen at the same time (they overlap), meaning they are **not mutually exclusive**.
   - Therefore, the correct answer is **c.** not mutually exclusive.
1. The sample points of $$ \mathrm{A} \cup \mathrm{B} $$ are $$ \{1,2,4,5,6,7,8,9\} $$. - **Answer:** b. $$ \{1,2,4,5,6,7,8,9\} $$ 2. The events are **not mutually exclusive** because they share common outcomes. - **Answer:** b. not mutually exclusive 3. The probability of drawing a club or a red card is $$ \frac{3}{4} $$. - **Answer:** a. $$ \frac{3}{4} $$ 4. The formula for the probability of mutually exclusive events is $$ \mathbf{P}(A)+\mathbf{P}(B) $$. - **Answer:** a. $$ \mathbf{P}(A)+\mathbf{P}(B) $$ 5. The events are **mutually exclusive** since they do not have common outcomes. - **Answer:** c. mutually exclusive 6. Attending an online class and using the internet at the same time are **not mutually exclusive** events. - **Answer:** c. not mutually exclusive

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