Meghan received a box of jelly beans for her birthday. The jelly beans in the box have five different flavors. The table below shows how many jelly beans of each flavor are in the box.
| Flavor | Number |
| -------- | ------ |
| Grape | 16 |
| Licorice | 10 |
| Cherry | 12 |
| Lemon | 14 |
| Lime | 8 |
The jelly beans are all the same shape and size. Meghan does not like grape or lime. What is the probability that she will pick a jelly bean from the full box that has a flavor she does like? Show and explain your work.
Answer (1)
Calculate the total number of jelly beans: 16 + 10 + 12 + 14 + 8 = 60 .
Calculate the number of jelly beans Meghan likes: 10 + 12 + 14 = 36 .
Calculate the probability: 60 36 .
Simplify the fraction: 5 3 .
Explanation
Understand the problem and provided data We are given a box of jelly beans with five different flavors: Grape (16), Licorice (10), Cherry (12), Lemon (14), and Lime (8). Meghan does not like grape or lime flavored jelly beans. We need to find the probability that she picks a jelly bean that she likes.
Calculate the total number of jelly beans First, we need to calculate the total number of jelly beans in the box. We add the number of jelly beans of each flavor:
T o t a l = 16 + 10 + 12 + 14 + 8 = 60
Calculate the number of jelly beans Meghan likes Next, we need to calculate the number of jelly beans that Meghan likes. She likes Licorice, Cherry, and Lemon. So we add the number of jelly beans of these flavors:
L ik e d = 10 + 12 + 14 = 36
Calculate the probability Now, we can calculate the probability that Meghan picks a jelly bean that she likes. This is the number of jelly beans she likes divided by the total number of jelly beans:
P ro babi l i t y = T o t a l L ik e d = 60 36
Simplify the fraction Finally, we simplify the fraction:
60 36 = 6 × 10 6 × 6 = 10 6 = 2 × 5 2 × 3 = 5 3
State the final answer Therefore, the probability that Meghan picks a jelly bean that she likes is 5 3 .
Examples
Imagine you have a bag of mixed candies, and you only like some of them. Calculating the probability of picking a candy you like helps you understand your chances of getting a favorable outcome each time you reach into the bag. This is useful in many real-life scenarios, such as estimating the likelihood of winning a prize in a raffle or drawing a specific card from a deck.
