Simulations to Estimate Probabilities Answers

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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
2
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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.
3

Twelve of the last 16 winners of the school science fair have been seventh grade students. Mona placed 3 red marbles and 1 green marble in a bag to create a simulation to predict whether future science fair winners will be seventh graders. According to Mona’s model, what is the probability that the next 4 winners will all be seventh grade students?

A
StartFraction 3 over 16 EndFraction
Option A
B
StartFraction 81 over 256 EndFraction
Option B
C
Three-fourths
Option C
D
StartFraction 7 over 8 EndFraction
Option D
4

Twelve of the 20 students in Ms. Sarno’s homeroom are female. Each month, Ms. Sarno randomly selects a student to act as “teacher’s helper.”Which simulation best models the selection of female “teacher’s helpers” for January, February, March, and April?

A
A spinner, divided into 5 congruent sectors with three of the sectors representing female students, is spun 12 times.
B
A coin, with heads up representing female students, is flipped 4 times.
C
A bag of 15 marbles, with 9 marbles representing female students, has a marble drawn 4 times with replacement.
D
A number cube, with odd numbers representing female students, is rolled 12 times.
5

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
6

Vinay constructed this spinner based on the population of teachers at his school.According to Vinay’s model, what is the probability that he will have a male history teacher two years in a row?

Question illustration
A
StartFraction 3 over 8 EndFraction
Option A
B
(StartFraction 3 over 8 EndFraction) (2)
Option B
C
(StartFraction 3 over 8 EndFraction) squared
Option C
D
StartFraction 3 over 8 squared EndFraction
Option D
7

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
8

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
9

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
10

Which statement best describes the use of a simulation to predict the probability that two randomly chosen people will both have their birthdays on a Monday?

A
Randomly generate an integer from 1 to 2 seven times, and the probability is .
Option A
B
Randomly generate an integer from 1 to 2 seven times, and the probability is .
Option B
C
Randomly generate an integer from 1 to 7 two times, and the probability is .
Option C
D
Randomly generate an integer from 1 to 7 two times, and the probability is .
Option D

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