Question 1

Question

A)Describe the following event as a subset of the set of all outcomes. If a deck of 52 cards is divided into two colors (red and black) and 4 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 list the outcomes for drawing a face card with a man on it.(1 point)
Responses

{King Hearts, King Diamonds, King Clubs, King Spades}
left brace King Hearts comma King Diamonds comma King Clubs comma King Spades right brace

{Jack Hearts, Jack Spades, King Hearts, King Spades}
left brace Jack Hearts comma Jack Spades comma King Hearts comma King Spades right brace

{Jack Hearts, King Hearts}
left brace Jack Hearts comma King Hearts right brace

{Jack Hearts, Jack Diamonds, Jack Clubs, Jack Spades, King Hearts, King Diamonds, King Clubs, King Spades}
left brace Jack Hearts comma Jack Diamonds comma Jack Clubs comma Jack Spades comma King Hearts comma King Diamonds comma King Clubs comma King Spades right brace
Question 2
A)Emory rolls a regular 10-sided number cube. List the outcomes for the event of rolling an even number <5.(1 point)
Responses

{6,8,10}
left brace 6 comma 8 comma 10 right brace

{4,5,6}
left brace 4 comma 5 comma 6 right brace

{2,4}
left brace 2 comma 4 right brace

{2,4,6,8,10}
left brace 2 comma 4 comma 6 comma 10 right brace
Question 3
A)
A spinner has six different colors, all of equal portions: red, yellow, blue, green, orange, and purple. You and a friend each spin the spinner six times and record your results. Following are the spins.

You: {red, yellow, red, orange, orange, red}

Friend: {blue, red, orange, purple, purple, red}

Describe which subset would be considered a union of the two events.

(1 point)
Responses

{blue, yellow}
left brace blue comma yellow right brace

{red, blue, yellow, orange, purple}
left brace red comma blue comma yellow comma orange comma purple right brace

{red, orange}
left brace red comma orange right brace

{green}
left brace green right brace
Question 4
A)Mischa is throwing a birthday party for her sister and decides to survey all who are attending on which ice cream flavor they prefer: chocolate, vanilla, strawberry, or a mix. She finds that 8 prefer chocolate, 6 prefer vanilla, 2 prefer strawberry, 14 prefer a mix of the three, and 3 don’t eat ice cream. If you were to draw a Venn diagram of your findings, which number would be located in the intersection of the three flavors?(1 point)
Responses

8
8

14
14

6
6

3
3
Question 5
A)
Sam and Silvie go bowling. The following table shows how many total pins they knocked down in each of the 10 frames.

Sam 5 6 7 8 10 9 4 10 4 6
Silvie 8 5 7 5 2 9 10 4 5 9
If the sample space is all of the possible numbers of pins that can be knocked down in a single frame, which subset would be considered a complement of the set of pins that Sam and Silvie knocked down?

(1 point)
Responses

{2,6}
left brace 2 comma 6 right brace

{1,2,3,4,5,6,7,8,9,10}
left brace 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 right brace

{2,4,5,6,7,8,9,10}

Answer 1

Here are the answers to each of your questions with explanations:

Question 1: The question asks for the outcomes of drawing a face card with a man on it from a standard deck of cards. The face cards with a man on them are the Kings and Jacks. Therefore, the set that includes all Kings and Jacks from all four suits is:

Response: {\[ \text{Jack Hearts, Jack Diamonds, Jack Clubs, Jack Spades, King Hearts, King Diamonds, King Clubs, King Spades} \]} Answer: {Jack Hearts, Jack Diamonds, Jack Clubs, Jack Spades, King Hearts, King Diamonds, King Clubs, King Spades}

Question 2: The question asks for rolling an even number less than 5 on a 10-sided number cube. The even numbers on this cube are 2, 4, 6, 8, and 10. The even numbers that are less than 5 are:

Response: {\[ \text{2, 4} \]} Answer: {2, 4}

Question 3: The union of two events is the set of all outcomes that appear in either event. From the given spins:

You: {red, yellow, red, orange, orange, red} → unique outcomes: {red, yellow, orange} Friend: {blue, red, orange, purple, purple, red} → unique outcomes: {blue, red, orange, purple}

The union of the two events is {red, yellow, orange, blue, purple}.

Response: {\[ \text{red, blue, yellow, orange, purple} \]} Answer: {red, blue, yellow, orange, purple}

Question 4: The question involves finding the number that should be in the intersection of the three flavors (chocolate, vanilla, strawberry). Since "14 prefer a mix of the three," and that’d be considered the intersection point where all three preferences overlap.

Response: Answer: 14

Question 5: The sample space of possible bowling scores in a single frame is from 0 to 10 (since you can't knock down more than 10 pins in a frame). Sam and Silvie knocked down various pins ranging from 2 to 10. The complement would be all numbers that are not represented in the scores they achieved.

The scores they achieved are all between 2 and 10, so the only possible score not represented is 1.

Response: {\[ \text{1,2,3,4,5,6,7,8,9,10} \]} Answer: {1,2,3,4,5,6,7,8,9,10}