Question

Evan randomly selects 30 marbles from a bag. His data is given in the table.

Color Number of Marbles
Red
9

White
3

Blue
8

Orange
4

Yellow
6

Based on Evan's data, enter a number in each box to complete the sentences correctly.
The probability of selecting a yellow marble is
.

If there are 300 marbles in the bag, a good estimate for the total number of red marbles in the bag is

Answer 1

To find the probability of selecting a yellow marble, we use the formula for probability:

\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]

In this case, the number of favorable outcomes for selecting a yellow marble is 6 (the number of yellow marbles), and the total number of marbles is 30.

So, the probability of selecting a yellow marble is:

\[
\text{Probability of yellow} = \frac{6}{30} = \frac{1}{5} = 0.2
\]

Now, to estimate the total number of red marbles in the bag if there are 300 marbles, we can set up a proportion based on Evan's sample:

The proportion of red marbles in the sample can be calculated as follows:

\[
\text{Fraction of red marbles} = \frac{9 \text{ (red marbles)}}{30 \text{ (total marbles)}} = \frac{9}{30} = 0.3
\]

Now, we can use this fraction to estimate the total number of red marbles in a bag of 300 marbles:

\[
\text{Estimated number of red marbles} = \text{Fraction of red marbles} \times \text{Total number of marbles in bag}
\]
\[
\text{Estimated number of red marbles} = 0.3 \times 300 = 90
\]

Putting it all together, the completed sentences are:

The probability of selecting a yellow marble is **0.2**.

If there are 300 marbles in the bag, a good estimate for the total number of red marbles in the bag is **90**.