AnswersTX-College Prep Math BProbability of Compound Events

Simulations to Estimate Probabilities Answers

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3

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.
5

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
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
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.

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