Question
A soda company decides to reward prizes to celebrate its 50th anniversary. They claim that 25% of all bottles produced this month contain winning prizes under each bottle cap. Mario wants to simulate randomly selecting 20 bottles to determine how many bottles contain a winning prize.
Determine the simulation that can be used to accurately model this situation.
Responses
In a bag, place 25 red chips to represent bottles with prizes and 25 white chips to represent bottles with no prizes. Pull out a chip, record its colour, and put it back. Repeat this 20 times, and count how many are red.
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In a bag, place 25 red chips to represent bottles with prizes and 75 white chips to represent bottles with no prizes. Pull out a chip, record its colour, and put it back. Repeat this 20 times, and count how many are red.
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In a bag, place numbered cards 1 to 26. Assign odd numbers to bottles with prizes and even numbers to bottles without prizes. Pull out a card, record the number, and do not put it back in the bag. Repeat this 20 times, and count how many are odd numbers.
In a bag, place numbered cards 1 to 26. Assign odd numbers to bottles with prizes and even numbers to bottles without prizes. Pull out a car, record the number, and put it back. Repeat this 20 times, and count how many are odd numbers.
Determine the simulation that can be used to accurately model this situation.
Responses
In a bag, place 25 red chips to represent bottles with prizes and 25 white chips to represent bottles with no prizes. Pull out a chip, record its colour, and put it back. Repeat this 20 times, and count how many are red.
.
In a bag, place 25 red chips to represent bottles with prizes and 75 white chips to represent bottles with no prizes. Pull out a chip, record its colour, and put it back. Repeat this 20 times, and count how many are red.
.
In a bag, place numbered cards 1 to 26. Assign odd numbers to bottles with prizes and even numbers to bottles without prizes. Pull out a card, record the number, and do not put it back in the bag. Repeat this 20 times, and count how many are odd numbers.
In a bag, place numbered cards 1 to 26. Assign odd numbers to bottles with prizes and even numbers to bottles without prizes. Pull out a car, record the number, and put it back. Repeat this 20 times, and count how many are odd numbers.
Answers
GPT-4o mini
To accurately model the situation where 25% of the soda bottles contain winning prizes, we need to represent the winning and non-winning bottles in accordance with this probability.
Since 25% indicates that for every 100 bottles produced, 25 should contain a prize, we can represent this in a smaller simulation.
The correct response would be:
**In a bag, place 25 red chips to represent bottles with prizes and 75 white chips to represent bottles with no prizes. Pull out a chip, record its colour, and put it back. Repeat this 20 times, and count how many are red.**
This method accurately simulates the randomness of selecting from the population of soda bottles, as it maintains the correct ratio of winning to non-winning bottles (25% winning). Each draw is independent since you are replacing the chip after each selection, which aligns with the concept of sampling with replacement.
Since 25% indicates that for every 100 bottles produced, 25 should contain a prize, we can represent this in a smaller simulation.
The correct response would be:
**In a bag, place 25 red chips to represent bottles with prizes and 75 white chips to represent bottles with no prizes. Pull out a chip, record its colour, and put it back. Repeat this 20 times, and count how many are red.**
This method accurately simulates the randomness of selecting from the population of soda bottles, as it maintains the correct ratio of winning to non-winning bottles (25% winning). Each draw is independent since you are replacing the chip after each selection, which aligns with the concept of sampling with replacement.