Question 1

Question

A)
Emilio rolls a typical 6-sided number cube. What are the possible outcomes for him to rool an even number that is divisible by 3?

(1 point)
Responses

{2,4,6}
{2,4,6}

{1,3,5}
{1,3,5}

{3}
{3}

{6}
{6}
Question 2
A)
In bowling, there are 10 pins that stand in a triangular shape. The goal is to knock down all the pins. You have two chances to roll the ball and knock down pins, if you don't knock all of them down on the first roll. Suppose on your first roll, you knock down the 2,3,5 and 10 pins. On your second roll you knock down the 6 and 7 pins. The pins are numbered as shown below.



(1 point)
Which of the following options is a subset that is a complement of the event?

Option #1: {2,3,5,6, 7,10}

Option # 2: {6,7}

Option # 3: {1,4,8,9}

Option #4: {2,3,5,10}



Option # $$ is a subset that is a complement of the event.

Question 3
A)
There are 52 cards in a standard deck, like the one pictured below. What is the probability of drawing a red 7 from a standard deck of cards?



(1 point)
Responses

152
1 over 52

352
3 over 52

113
1 over 13

126
1 over 26
Question 4
A)
Lucia has a spinner with the numbers 1-8 on it and a number cube with the numbers 1 - 6. Let event A represent landing on a number greater than 3 on the spinner and event B represent rolling a number greater than 3 on the number cube. See the pictures below as an example. Make sure to enter your answer as a fraction.

(1 point)


What is P(A∩B) =
$$





Question 5
A standard deck of cards has 52 card. The 52 cards are divided into 4 units: diamonds, clubs, hearts, and spades. The diamond and the hearts are red cards and the clubs and the spades are black. See the picture below for an example. For the following problems, consider the following scenario: Brant is doing a card trick and asks you to pick a card from a standard deck. Let event A be that you choose an ace and let event B be that you choose a red card.
A)Determine the following . Enter your answer as a fraction(3 points)
P (A ∩ B)
$$

P(A) = $$

P (B) = $$

B)True or False: In the given situation, events A and B are dependent.(1 point)
Responses

True
True

False
False
Question 6
A)Brinsley has a jar that has 20 marbles in it: 4 red, 4 blue, 4 green, 4 yellow and 4 purple. What is the probability of her selecting a red marble, not replacing it, and then drawing a green marble?(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Probability is Response area
Question 7
Use the following situtation to answer the questions: At the library, there are 50 books on a shelf. There are 8 romance novels, 12 historical fiction novels, 15 mystery novels and 15 nonfiction books. Ravi must choose 2 books and doesn't really care which kind they are. He decides to randomly pick 1 and then pick another without replacement.



A)What is the probability of selecting a historical fiction book and then a romance novel?(1 point)
Responses

1250×850
12 over 50 times 8 over 50

850
8 over 50

1250
12 over 50

1250×849
12 over 50 times 8 over 49
B)What is the probability that he pics a nonfiction book and then a mystery novel?(1 point)
Responses

1550×1549
15 over 50 times 15 over 49

1549
15 over 49

1550×1550
15 over 50 times 15 over 50

1550
15 over 50
Question 8
Parker is organizing a race. Only the top 5 will be awarded money as follows: 1st place = $1,000; 2nd place = $800; 3rd place = $600; 4th place = $400; and 5th place = $200.

A)If 20 total athletes enter the race, how many ways can the prizes be allocated?(1 point)
Responses

5,587,021,440
5,587,021,440

1,860,480
1,860,480

6
6

15,504
15,504
B)If only 10 people enter the race, how many ways can the prizes be allocated?(1 point)
$$ ways (type as a number only, no commas or symbols)
Question 9
A)How many different ways are there to choose 5 books from a shelf of 24 books if the order in which they are selected doesn't matter?(1 point)
Responses

5,100,480
5,100,480

7 13
7 13

42,504
42,504

22
22
B)How many ways are there if the order does matter?(1 point)
Responses

42,504
42,504

5,100,480
5,100,480

22
22

7 13
7 13
Question 10
A)
Circle A is inscribed inside of Trapezoid EFGH. What is the probability that a point placed randomly in the figure is inside the circle? The drawing is not drawn to scale.

(1 point)
Responses

.95
.95

.05
.05

.24
.24

.76

Answer 1

Sure! Here are the answers to your questions:

Question 1: Emilio rolls a typical 6-sided number cube. The possible outcomes for him to roll an even number that is divisible by 3 are only {6}.

Question 2: You have two rolls knocking down pins: {2,3,5,10} and {6,7}. The total pins are {1,2,3,4,5,6,7,8,9,10}. The complement of event (knocking down the selected pins) contains the pins that were not knocked down, which are {1,4,8,9}. Therefore, the answer is Option #3: {1,4,8,9}.

Question 3: In a standard deck of cards, there are 2 red 7s (one from diamonds and one from hearts). Thus, the probability of drawing a red 7 is 2/52, which simplifies to 1/26.

Question 4: Event A (spinner numbers greater than 3) results in {4, 5, 6, 7, 8} which has 5 favorable outcomes. Event B (cube numbers greater than 3) results in {4, 5, 6} which has 3 favorable outcomes. By multiplying probabilities: P(A) = 5/8 P(B) = 3/6 = 1/2 P(A∩B) = P(A) * P(B) = (5/8) * (1/2) = 5/16.

Question 5: A)

• P(A ∩ B): There are 2 aces that are red. Probability = 2/52 = 1/26.
• P(A): There are 4 aces in total. Probability = 4/52 = 1/13.
• P(B): There are 26 red cards in total. Probability = 26/52 = 1/2.

B) True. Events A and B are dependent since knowing that a red card is drawn changes the probability of drawing an ace.

Question 6: The probability of drawing a red marble first (4 red out of 20) is 4/20. If a red marble is drawn, then there are 19 marbles left where the probability of drawing a green marble next (4 out of 19) is 4/19. Therefore, the combined probability is: P(red then green) = (4/20) * (4/19) = 16/380 = 4/95.

Question 7: A) The probability of selecting a historical fiction book (12 out of 50) and then a romance novel (8 out of 49) is: P = (12/50) * (8/49) = 96/2450 = 48/1225.

B) For selecting a nonfiction book (15 out of 50) first and then a mystery novel (15 out of 49): P = (15/50) * (15/49) = 225/2450 = 45/490.

Question 8: A) The total ways to allocate prizes to 20 athletes (permutations) is: P(20,5) = 20! / (20-5)! = 20! / 15! = 20 * 19 * 18 * 17 * 16 = 1860480.

B) If only 10 people enter, the ways to allocate prizes is: P(10,5) = 10! / (10-5)! = 10! / 5! = 10 * 9 * 8 * 7 * 6 = 30240.

Question 9: A) To choose 5 books from 24 without regard to order, you would compute combinations. \( C(24,5) \): C(24,5) = 24!/(5!(24-5)!) = 42504. So, the answer is 42504.

B) If order matters, you would use permutations: P(24,5) = 24! / (24-5)! = 24 * 23 * 22 * 21 * 20 = 42504.

Question 10: For the probability that a random point in the figure (trapezoid) is inside the circle inscribed within it, this depends on the ratio of the area of the circle to the area of the trapezoid. If we don't have specific measurements or ratios, an estimate of the probability could be given; let's say 0.24 (assuming based on some geometrical intuition).

If you have any follow-up questions or need clarifications, feel free to ask!