Question 1

Question

A)
If a deck of 52 cards is divided into two colors (red and black) and has four suits (the red suits diamonds and hearts and the black suits spades and clubs) with 13 different values per suit (Ace, numbers 2 through 10, Jack, Queen, and King), then what are the outcomes for drawing a red King?

Option #1: {King Hearts, King Diamonds}

Option #2: {King Spades, King Clubs}

Option #3: {King Hearts, King Diamonds, King Spades, King Clubs}

Option #4: {King Hearts}

(1 point)
The correct answer is Option #$$.
Question 2
A)
If a typical 6-sided number cube is rolled, then list the outcomes for the event of rolling an odd number >3.

Option #1: {1,3}

Option #2: {∅}

Option #3: {4,5,6}

Option #4: {5}

(1 point)
The correct answer is Option #$$.
Question 3
A)
A bag has 12 numbered marbles inside, numbered 1–12. Without looking, you reach in and pull out one marble at a time, without returning the marble to the bag. The numbers you draw are 2, 5, and 11. Which of the following options describes the complement of the event of the numbers you drew?

Option #1: {empty set}

Option #2: {2,5,11}

Option #3: {1,3,4,6,7,8,9,10,12}

(1 point)
Option #$$ describes the complement of the event.
Question 4
A)
You and your friend are playing a game with two number cubes. If you roll doubles or two numbers that are both even, you get to take another turn and roll again. Which of the following options is a subset for either rolling doubles or both numbers being even?

Option #1: {evens}∪{doubles}

Option #2: {evens}∩{doubles}

Option #3: {1,2,3,4,5}

(1 point)
Option #$$ is a subset for rolling two number cubes showing even numbers or doubles.
Question 5
A)
In bowling, there are 10 pins that stand in a triangular shape. The idea is to knock down all the pins. A frame consists of two rolls (if you don’t knock all 10 pins down in the first roll). On your first roll, you knock down pins 2, 5, 8, and 10; in the second roll, you knock down pins 1 and 7. If the pins knocked down in each roll are considered separate events, which of the following options describes an intersection of the two events?

Option #1: {3,4,6,9}

Option #2: {1,2,5,7,8,10}

Option #3: {empty set}

(1 point)

Answer 1

Let's address each question in sequence.

Question 1: You are asked for the outcomes of drawing a red King. The red suits are hearts and diamonds, and there are Kings in both.

The correct answer is: Option #1: {King Hearts, King Diamonds}

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Question 2: You need to find the outcomes for rolling an odd number greater than 3 on a 6-sided die. The odd numbers are 1, 3, and 5, and out of those, only 5 is greater than 3.

The correct answer is: Option #4: {5}

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Question 3: The complement of the event of drawing marbles numbered 2, 5, and 11 means listing all the numbers that are not in the drawn set. The total numbers are 1 to 12, so the complement will be 1, 3, 4, 6, 7, 8, 9, 10, 12.

The correct answer is: Option #3: {1,3,4,6,7,8,9,10,12}

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Question 4: You are asked for a subset that describes rolling either doubles or both numbers being even. The options suggest using union or intersection. The correct interpretation would be the union of both sets (rolling doubles or rolling even numbers), as it captures either event.

The correct answer is: Option #1: {evens}∪{doubles}

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Question 5: You need to identify an intersection of the events from the bowling scenario. The intersection refers to pins knocked down in both rolls. The first roll knocks down pins 2, 5, 8, and 10, and the second roll knocks down pins 1 and 7. There are no pins in common between the two rolls.

The correct answer is: Option #3: {empty set}

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So, summarizing the correct answers:

• Question 1: Option #1
• Question 2: Option #4
• Question 3: Option #3
• Question 4: Option #1
• Question 5: Option #3