Sara and her friends are enjoying a bag of candy-coated chocolates. Just for fun, they remove 80 pieces of candy from the bag to check their color. The outcomes are shown in the table.
| Candy Color | Number of Candies |
| :-------------- | :---------------- |
| brown or orange | 25 |
| green or yellow | 28 |
| red or blue | 27 |
Which statement is true based on the results in the table?
A. All of the outcomes are equally likely because their relative frequencies are similar.
B. All of the outcomes are equally likely because the relative frequency of picking brown or orange candies is greater than that of picking green or yellow.
C. All of the outcomes are not equally likely because there is a lot of variation in their relative frequencies.
D. All of the outcomes are not equally likely because the relative frequency of picking green or yellow candies is the highest.
E. All of the outcomes are not equally likely because the relative frequency of picking red or blue candies is less than that of picking brown or orange or green or yellow candies.
Answer (2)
Calculate the relative frequency of brown or orange candies: 80 25 = 0.3125 .
Calculate the relative frequency of green or yellow candies: 80 28 = 0.35 .
Calculate the relative frequency of red or blue candies: 80 27 = 0.3375 .
Since the relative frequencies are not equal, the outcomes are not equally likely. Therefore, the correct answer is C: All of the outcomes are not equally likely because there is a lot of variation in their relative frequencies. C
Explanation
Analyze the problem and data We are given the number of candies for each color combination out of a sample of 80 candies. To determine which statement is true, we need to calculate the relative frequencies of each color combination.
Calculate relative frequency of brown or orange The relative frequency of brown or orange candies is 80 25 = 0.3125 .
Calculate relative frequency of green or yellow The relative frequency of green or yellow candies is 80 28 = 0.35 .
Calculate relative frequency of red or blue The relative frequency of red or blue candies is 80 27 = 0.3375 .
Compare the relative frequencies Now, let's compare the relative frequencies. We have 0.3125, 0.35, and 0.3375. These values are somewhat close, but not equal. Therefore, the outcomes are not equally likely. The highest relative frequency is 0.35 (green or yellow), and the lowest is 0.3125 (brown or orange).
Determine the correct statement Based on our calculations and comparisons, the statement that is true is: All of the outcomes are not equally likely because there is some variation in their relative frequencies.
Examples
Understanding relative frequencies can help in various real-life scenarios. For example, if a company wants to determine which product color is most popular among customers, they can collect data on customer preferences and calculate the relative frequencies of each color. This information can then be used to make informed decisions about product design and marketing strategies. Another example is in weather forecasting, where relative frequencies of different weather conditions can be used to predict future weather patterns.
The outcomes based on the candy color distribution are not equally likely since the calculated relative frequencies differ. The highest frequency is for green or yellow candies, and the lowest is for brown or orange candies. Thus, the correct answer is option C.
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