Maria pulls colored marbles out of a bag one at a time. Her results are shown in the table below.

Color Outcomes
Blue 36
Yellow 42
Black 18
White 24

Based on the outcomes, if 20 more marbles are pulled out of the bag and replaced, how many marbles can be expected to be white?
A.
1

B.
4

C.
5

D.
6

1 answer

To find the expected number of white marbles when Maria pulls out 20 more marbles, we first need to determine the total number of marbles currently observed and the proportion of white marbles.

The outcomes show the following counts for each color:

  • Blue: 36
  • Yellow: 42
  • Black: 18
  • White: 24

First, we can calculate the total number of marbles:

\[ \text{Total marbles} = 36 + 42 + 18 + 24 = 120 \]

Next, we calculate the proportion of white marbles:

\[ \text{Proportion of white marbles} = \frac{\text{Number of white marbles}}{\text{Total number of marbles}} = \frac{24}{120} = \frac{1}{5} = 0.20 \]

Now, we can use this proportion to find the expected number of white marbles in the next 20 pulls.

The expected number of white marbles when 20 more are pulled is given by:

\[ \text{Expected number of white marbles} = \text{Proportion of white marbles} \times \text{Number of pulls} = 0.20 \times 20 = 4 \]

Thus, the expected number of white marbles is:

\[ \boxed{4} \]