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. $$ \{1,2,4,6,8,9\} $$ d. $$ \{1,5\} $$ These events have common outcomel. a. mutually exclusive b. not mutually exclusive c. complement d. intersection When you draw a card form a standard deck of cards, what is the probability of getting a club or a red cand? a $$ \frac{3}{4} $$ b. $$ \frac{31}{82} $$ c. $$ \frac{1}{4} $$ d. $$ \frac{13}{82} $$ Which of the following is the formula for probability of mutually exclusive events? a. $$ \mathbf{P}(A)+\mathbf{P}(B) $$ b. $$ P(A)+P(B)+P(A \cap B) \in P(A) $$ - $$ P(B) $$ d. $$ P(A){ }^{*} P(B) $$ These events do not have common outcomels. a. not mutually exclusive b. complement c. mutually exclusive 4. internection What kind of events are boing 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. Sample Points of $$ \mathrm{A} \cup \mathrm{B} $$

Given:
- $$ \mathrm{A} = \{1, 2, 5, 7, 8\} $$
- $$ \mathrm{B} = \{2, 4, 6, 8, 9\} $$

The union of two sets $$ \mathrm{A} \cup \mathrm{B} $$ includes all unique elements from both sets.

Calculating $$ \mathrm{A} \cup \mathrm{B} $$:
- Combine the elements: $$ \{1, 2, 5, 7, 8\} $$ and $$ \{2, 4, 6, 8, 9\} $$
- Remove duplicates: $$ \{1, 2, 4, 5, 6, 7, 8, 9\} $$

Thus, 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. Common Outcomes

Since both sets $$ \mathrm{A} $$ and $$ \mathrm{B} $$ have common elements (2 and 8), they are not mutually exclusive.

**Answer:** b. not mutually exclusive

### 3. Probability of Getting a Club or a Red Card

In a standard deck of cards:
- There are 52 cards in total.
- There are 13 clubs.
- There are 26 red cards (13 hearts + 13 diamonds).

The probability of getting a club or a red card can be calculated as follows:
- Total unique outcomes for clubs and red cards: $$ 13 + 26 = 39 $$
- Probability: $$ P(	ext{Club or Red}) = \frac{39}{52} = \frac{3}{4} $$

**Answer:** a. $$ \frac{3}{4} $$

### 4. Formula for Probability of Mutually Exclusive Events

For mutually exclusive events, the probability is simply the sum of the probabilities of each event:
- $$ P(A \cup B) = P(A) + P(B) $$

**Answer:** a. $$ \mathbf{P}(A)+\mathbf{P}(B) $$

### 5. Events Illustrated by Attending an Online Class or Using the Internet

Attending an online class and using the internet at the same time are events that can occur together, meaning they are not mutually exclusive.

**Answer:** c. not mutually exclusive

In summary:
1. b. $$ \{1,2,4,5,6,7,8,9\} $$
2. b. not mutually exclusive
3. a. $$ \frac{3}{4} $$
4. a. $$ \mathbf{P}(A)+\mathbf{P}(B) $$
5. c. not mutually exclusive
1. The sample points of $$ \mathrm{A} \cup \mathrm{B} $$ are $$ \{1,2,4,5,6,7,8,9\} $$. 2. The events are not mutually exclusive. 3. The probability of getting a club or a red card is $$ \frac{3}{4} $$. 4. The formula for the probability of mutually exclusive events is $$ P(A) + P(B) $$. 5. Attending an online class and using the internet at the same time are not mutually exclusive events.

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Solution

1. Sample Points of

2. Common Outcomes

3. Probability of Getting a Club or a Red Card

4. Formula for Probability of Mutually Exclusive Events

5. Events Illustrated by Attending an Online Class or Using the Internet

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