Ava has a bag of 500 jelly beans of different colors. She randomly draws out 20 jelly beans and records their colors.

Color Number
red 5
pink 4
purple 4
orange 3
yellow 2
green 2
Based on the data, estimate how many orange jelly beans are in the bag.
____orange jelly beans

1 answer

To estimate the number of orange jelly beans in the bag, we can use the proportion of orange jelly beans drawn in Ava's sample of 20 jelly beans.

In Ava's sample, there were 3 orange jelly beans out of 20 total jelly beans:

\[ \text{Proportion of orange beans} = \frac{\text{Number of orange jelly beans in sample}}{\text{Total jelly beans in sample}} = \frac{3}{20} \]

Next, we'll use this proportion to estimate the total number of orange jelly beans in the bag of 500 jelly beans. We set up the following equation:

\[ \text{Estimated number of orange jelly beans} = \text{Total jelly beans} \times \text{Proportion of orange jelly beans} \]

Substituting in the values:

\[ \text{Estimated number of orange jelly beans} = 500 \times \frac{3}{20} \]

Now, we calculate it:

\[ 500 \times \frac{3}{20} = 500 \times 0.15 = 75 \]

Therefore, the estimated number of orange jelly beans in the bag is:

\[ \boxed{75} \text{ orange jelly beans} \]