Answer: To estimate the probability of having at least one left-handed person in a random group of three people, Jocelyn should create a simulation using a bag of marbles as described.
Since Jocelyn wants to represent left-handed people with yellow marbles and right-handed people with red marbles, she starts with one yellow marble in the bag (to represent the possibility of having at least one left-handed person in the group of three). Now, she needs to determine the number of red marbles (right-handed people) to add to the bag.
To create a group of three people, Jocelyn draws one marble at random three times, with replacement (meaning she puts the marble back in the bag after each draw). Each draw represents one person in the group.
To ensure the simulation is accurate and reflects the approximate 12.5% left-handed population, Jocelyn needs to have the same proportion of yellow (left-handed) and red (right-handed) marbles in the bag as the proportion of left-handed and right-handed people in the population.
Since the left-handed proportion is 12.5%, the right-handed proportion is 100% - 12.5% = 87.5%.
Now, let's calculate the number of red marbles (right-handed people) to add to the bag:
Number of red marbles = (Right-handed proportion / Left-handed proportion) * Number of yellow marbles
Number of red marbles = (87.5% / 12.5%) * 1
Number of red marbles = (7/1) * 1
Number of red marbles = 7
So, Jocelyn should add 7 red marbles to her bag to represent the right-handed people, and the total number of marbles in the bag would be 1 yellow (left-handed) and 7 red (right-handed) marbles. This will give her a simulation that closely reflects the proportion of left-handed and right-handed people in the US population.