Simulations to Estimate Probabilities Answers

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The manager of a video game store found that 35 of the 140 people who preordered the latest baseball game canceled their orders the day before the game was released. He used that data to create a simulation to predict the probability that future customers will cancel their preorders. According to the manager’s model, what is the probability that two customers who preorder the newest golf game will both cancel their orders the day before the game is released?

A
StartFraction 1 over 16 EndFraction
Option A
B
StartFraction 1 over 8 EndFraction
Option B
C
One-fourth
Option C
D
One-half
Option D
2
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Ava surveyed the students in her homeroom about their footwear. She found that 12 students were wearing sneakers, 4 students were wearing boots, and 6 students were wearing dress shoes. She used this data to create a tool that would predict the footwear of randomly chosen students in the school. She placed 2 blue marbles, 3 red marbles, and 6 yellow marbles in a bag, and selected one marble, with replacement, for each student.What is the predicted footwear of three randomly chosen students if Ava drew two yellow marbles and 1 blue marble?

A
2 students wearing boots and 1 student wearing sneakers
B
2 students wearing sneakers and 1 student wearing boots
C
2 students wearing dress shoes and 1 student wearing boots
D
2 students wearing sneakers and 1 student wearing dress shoes
3

Theo is using this spinner to predict the favorite movie genre of randomly chosen students in his school.If Theo spins the spinner 60 times, how many times should he expect it to land on “Action”?

Question illustration
A
10
B
12
C
15
D
20
4

Sixteen of the 24 schools in Ryan’s county are public schools. Ryan used this spinner to predict the probability that the winner of the county spelling bee in each of the next four years will attend a private school.Which set of outcomes from Ryan’s simulation implies that the winner will attend a private school at least three times in that span? Select two options.

Question illustration
A
A-A-A-A
B
B-B-A-B
C
A-B-A-B
D
A-B-B-B
E
B-A-B-A
5

A restaurant owner has found that 80% of her customers return to the restaurant within two weeks. She wants to create a tool that will simulate the habits of her customers and allow her to predict the probability that three of the next four customers to visit her restaurant will return within two weeks.Which spinner simulation uses an appropriate device and has the correct number of trials?

A
a spinner divided into 5 congruent sectors, spun 3 times
B
a spinner divided into 5 congruent sectors, spun 4 times
C
a spinner divided into 2 congruent sectors, spun 3 times
D
a spinner divided into 2 congruent sectors, spun 4 times
6

Reese is using a coin to predict the gender of the puppies born to her dog. According to Reese’s model, which is the probability that a litter of 5 puppies will be all males?

A
StartFraction 1 over 32 EndFraction
Option A
B
StartFraction 1 over 16 EndFraction
Option B
C
StartFraction 1 over 10 EndFraction
Option C
D
One-half
Option D
7

The students at Southern Junior High School are divided into four homerooms. Benjamin just moved into the school district and will be randomly assigned to one homeroom. Which methods can be used to simulate this situation? Select three options..

A
Flip a coin 4 times, once for each homeroom, with heads up representing being assigned to the homeroom represented by that flip.
B
Draw a marble from a bag containing 5 white marbles, 5 black marbles, 5 red marbles, and 5 green marbles, with each color representing a different homeroom.
C
Use a random number generator with 1, 2, and 12 representing the first homeroom, 7, 9, and 10 representing the second homeroom, 3, 8, and 11 representing the third homeroom, and 4, 5, and 6 representing the fourth homeroom.
D
Roll a number cube with 1 representing the first homeroom, 2 representing the second homeroom, 3 representing the third homeroom, and any other outcome representing the fourth homeroom.
E
Spin a spinner with 8 congruent sections with 2 sections assigned to each homeroom.
8

Tyler believes that an 8-sided die can be used to predict whether customers at his store will use a coupon when making their purchases, with a roll of 1 indicating a coupon and all other outcomes indicating no coupon. Today, 4 of the first 48 customers in the store used a coupon. How does the experimental probability of a customer using a coupon compare to the theoretical probability of Tyler’s die?

A
The experimental probability is greater than the theoretical probability by more than 2%.
B
The experimental probability is less than the theoretical probability by more than 2%.
C
The experimental probability is greater than the theoretical probability, but within 2%.
D
The experimental probability is less than the theoretical probability, but within 2%.
9

April and Sanjay are both using tools to simulate the probability that a family with three children will have exactly one girl. April is using a coin, with tails up representing a boy and heads up representing a girl. She flipped the coin three times. Sanjay rolled a number cube three times with odd numbers representing a boy and even numbers representing a girl.Which statement best describes their simulations?

A
Both simulations have the same theoretical probability of a 3-child family having exactly one girl, but their experimental probabilities may differ.
B
The simulations have different theoretical probabilities of a 3-child family having exactly one girl, and the experimental probabilities they generate may differ.
C
The simulations have different theoretical probabilities of a 3-child family having exactly one girl, but their experimental probabilities will be the same.
D
Both simulations have the same theoretical probability of a 3-child family having exactly one girl, and their experimental probabilities will be the same.
10

Twelve of the 20 students in Mr. Skinner’s class brought lunch from home. Fourteen of the 21 students in Ms. Cho’s class brought lunch from home. Siloni is using two 15-section spinners to simulate randomly selecting students from each class and predicting whether they brought lunch from home or will buy lunch in the cafeteria.If each spinner is divided into 15 congruent sectors, how does the spinner representing Mr. Skinner’s class differ from the spinner representing Ms. Cho’s class?

A
One more sector of the Skinner-class spinner will represent bringing lunch from home.
B
One fewer sector of the Skinner-class spinner will represent bringing lunch from home.
C
Two more sectors of the Skinner-class spinner will represent bringing lunch from home.
D
Two fewer sectors of the Skinner-class spinner will represent bringing lunch from home.

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