A kiddie pool holds miniature plastic ducks in different colors. Sophia randomly picks up a duck and then replaces it. She repeats this process 100 times. The table shows the results of her experiment.
| Duck Color | Times Picked |
| ---------- | ------------ |
| red | 30 |
| green | 20 |
| yellow | 40 |
| blue | 10 |
What is the relative frequency of choosing a red duck? What color of duck is there likely to be the most of in the pool?
A. The relative frequency is 0.3. It is likely that most ducks are blue.
B. The relative frequency is 0.2. It is likely that most ducks are yellow.
C. The relative frequency is 0.3. It is likely that most ducks are yellow.
D. The relative frequency is 0.2. It is likely that most ducks are green.
Answer (2)
Calculate the relative frequency of red duck: 100 30 = 0.3 .
Identify the most frequently picked color: yellow (40 times).
Conclude that the relative frequency of red is 0.3 and yellow is likely the most abundant.
The answer is: C .
Explanation
Analyze the problem First, let's analyze the problem. We are given the number of times each color of duck was picked in an experiment where a duck is picked randomly and then replaced. We need to find the relative frequency of picking a red duck and determine which color of duck is most likely to be the most abundant in the pool.
Calculate the relative frequency of red duck The relative frequency of an event is calculated by dividing the number of times the event occurred by the total number of trials. In this case, the event is picking a red duck, which occurred 30 times out of 100 trials. So, the relative frequency of picking a red duck is: 100 30 = 0.3
Determine the most frequent color To determine which color of duck is likely to be the most abundant in the pool, we look at the number of times each color was picked. The color that was picked most frequently is likely to be the most abundant. From the table, we see that yellow was picked 40 times, which is more than any other color.
State the final answer Therefore, the relative frequency of choosing a red duck is 0.3, and it is likely that most ducks are yellow. This corresponds to option C.
Examples
Understanding relative frequencies can help in various real-life scenarios. For example, if a company wants to know which product is most popular among customers, they can conduct a survey and calculate the relative frequency of each product being chosen. This information can then be used to make decisions about which products to stock more of or which products to promote more heavily. Similarly, in elections, the relative frequency of votes for each candidate can help predict the outcome of the election.
The relative frequency of choosing a red duck is 0.3, and yellow is likely the most abundant color in the pool. The correct answer is option C.
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