A Package Contains 4 Red, 2 Green, 8 Purple, And 6 Blue Jelly Beans. What Is The Probability Of Choosing A Purple Jelly Bean, Eating It, And Then Choosing A Blue Jelly Bean?A. $\frac{1}{400}$ B. $\frac{1}{380}$ C.
A Package of Jelly Beans: Calculating the Probability of Choosing a Purple and Then a Blue Jelly Bean
In this article, we will explore the concept of probability and how it applies to a real-world scenario involving a package of jelly beans. We will calculate the probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean. This problem requires us to understand the concept of conditional probability and how to apply it to a series of events.
The package contains 4 red, 2 green, 8 purple, and 6 blue jelly beans. Let's start by calculating the total number of jelly beans in the package.
- Red jelly beans: 4
- Green jelly beans: 2
- Purple jelly beans: 8
- Blue jelly beans: 6
Total number of jelly beans: 4 + 2 + 8 + 6 = 20
To calculate the probability of choosing a purple jelly bean, we need to divide the number of purple jelly beans by the total number of jelly beans.
Probability of choosing a purple jelly bean = Number of purple jelly beans / Total number of jelly beans = 8 / 20 = 0.4 = 40%
Since we are assuming that the jelly bean is eaten after it is chosen, we need to consider the probability of eating the purple jelly bean. In this case, the probability of eating the purple jelly bean is 1, since it is certain that the jelly bean will be eaten.
After eating the purple jelly bean, we are left with 19 jelly beans in the package. The number of blue jelly beans remains the same, which is 6. To calculate the probability of choosing a blue jelly bean, we need to divide the number of blue jelly beans by the total number of jelly beans remaining in the package.
Probability of choosing a blue jelly bean = Number of blue jelly beans / Total number of jelly beans remaining = 6 / 19 = 0.3158 = 31.58%
To calculate the overall probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean, we need to multiply the probabilities of each event.
Overall probability = Probability of choosing a purple jelly bean × Probability of eating the purple jelly bean × Probability of choosing a blue jelly bean = 0.4 × 1 × 0.3158 = 0.12632 = 12.632%
In conclusion, the probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean is approximately 12.632%. This problem requires us to understand the concept of conditional probability and how to apply it to a series of events. By breaking down the problem into smaller events and calculating the probability of each event, we can arrive at the overall probability of the desired outcome.
The correct answer is C.
A Package of Jelly Beans: Calculating the Probability of Choosing a Purple and Then a Blue Jelly Bean - Q&A
In our previous article, we explored the concept of probability and how it applies to a real-world scenario involving a package of jelly beans. We calculated the probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean. In this article, we will answer some frequently asked questions related to this problem.
A: The total number of jelly beans in the package is 20. This includes 4 red, 2 green, 8 purple, and 6 blue jelly beans.
A: To calculate the probability of choosing a purple jelly bean, you need to divide the number of purple jelly beans by the total number of jelly beans.
Probability of choosing a purple jelly bean = Number of purple jelly beans / Total number of jelly beans = 8 / 20 = 0.4 = 40%
A: Since we are assuming that the jelly bean is eaten after it is chosen, the probability of eating the purple jelly bean is 1. This is because it is certain that the jelly bean will be eaten.
A: After eating the purple jelly bean, we are left with 19 jelly beans in the package. The number of blue jelly beans remains the same, which is 6. To calculate the probability of choosing a blue jelly bean, you need to divide the number of blue jelly beans by the total number of jelly beans remaining in the package.
Probability of choosing a blue jelly bean = Number of blue jelly beans / Total number of jelly beans remaining = 6 / 19 = 0.3158 = 31.58%
A: To calculate the overall probability, you need to multiply the probabilities of each event.
Overall probability = Probability of choosing a purple jelly bean × Probability of eating the purple jelly bean × Probability of choosing a blue jelly bean = 0.4 × 1 × 0.3158 = 0.12632 = 12.632%
A: The correct answer is C. .
A: The probability of choosing a purple jelly bean is 40%, but this does not mean that the probability of choosing a purple jelly bean and then a blue jelly bean is also 40%. This is because the probability of choosing a blue jelly bean after eating the purple jelly bean is not 100%. In fact, it is 31.58%. Therefore, the overall probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean is 12.632%.
In conclusion, we have answered some frequently asked questions related to the problem of calculating the probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean. We hope that this article has provided you with a better understanding of the concept of probability and how it applies to real-world scenarios.