Question

You are the marketing manager at The Best Candy Shop where the top sales item is the Dream Pop bags of flavored candies. You have been getting complaints from customers that there are not enough lemon or blueberry flavored candies, which are favorites, and too many grape and strawberry flavored candies. Your boss wants you to create an advertisement indicating, “all bags have equally likely flavors.” (That is, the probability of getting a strawberry flavored candy piece is the same as getting a blueberry flavored piece, etc.). As the marketing manager, you want to make sure you are advertising truthful information, so you pull a sample bag of Dream Pop candy and find the following pieces: 16 grape flavors 12 strawberry flavors 6 lemon flavors 6 blueberry flavors Explain how you could communicate to your boss that his advertising suggestion (all bags agave equally likely flavors) would be incorrect. You must include at least two (2) probabilities from your sample bag of candy that would deem his advice inaccurate.

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Answer to a math question You are the marketing manager at The Best Candy Shop where the top sales item is the Dream Pop bags of flavored candies. You have been getting complaints from customers that there are not enough lemon or blueberry flavored candies, which are favorites, and too many grape and strawberry flavored candies. Your boss wants you to create an advertisement indicating, “all bags have equally likely flavors.” (That is, the probability of getting a strawberry flavored candy piece is the same as getting a blueberry flavored piece, etc.). As the marketing manager, you want to make sure you are advertising truthful information, so you pull a sample bag of Dream Pop candy and find the following pieces: 16 grape flavors 12 strawberry flavors 6 lemon flavors 6 blueberry flavors Explain how you could communicate to your boss that his advertising suggestion (all bags agave equally likely flavors) would be incorrect. You must include at least two (2) probabilities from your sample bag of candy that would deem his advice inaccurate.

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108 Answers

To demonstrate that the assumption of equally likely flavors in all bags is incorrect, calculate the probabilities of getting a grape flavor and a blueberry flavor from the sample bag of Dream Pop candy.

Given that the sample bag contains:
- 16 grape flavors
- 12 strawberry flavors
- 6 lemon flavors
- 6 blueberry flavors

The probability of selecting a lemon-flavored candy from the sample bag is calculated as:

P(\text{Grape flavor})=\frac{\text{Number of grape flavors}}{\text{Total number of candy flavors}}=\frac{16}{16+12+6+6}=\frac{16}{40}=0.4

The probability of selecting a blueberry-flavored candy from the sample bag is calculated as:

P(\text{Blueberry flavor})=\frac{\text{Number of blueberry flavors}}{\text{Total number of candy flavors}}=\frac{6}{16 + 12 + 6 + 6}=\frac{6}{40}=0.15

Comparing the probabilities of grape and blueberry flavors would reveal that all flavors are not equally likely in the sample bag. Therefore, claiming that all bags have equally likely flavors would be misleading based on the provided sample data.

Answer: The calculated probabilities of grape (0.4) and blueberry (0.15) flavors show that not all flavors are equally likely in the sample bag, which would make the advertising claim inaccurate.

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