To find the number of yellow tiles in the bag, we first need to analyze the data provided for the pulls. We know the following:
- Total pulls: 100
- Blue tiles: 24
- Green tiles: 12
- Red tiles: 12
From this information, we can calculate the total number of tiles that have been counted:
\[ \text{Total counted tiles} = \text{Blue} + \text{Green} + \text{Red} = 24 + 12 + 12 = 48 \]
Since there are 100 tiles pulled and the number above represents the count for blue, green, and red tiles, we can find the number of yellow tiles by subtracting the counted tiles from the total pulls:
\[ \text{Total yellow tiles counted} = \text{Total pulls} - \text{Total counted tiles} = 100 - 48 = 52 \]
However, this number (52) doesn't make sense, as it exceeds 10, the total number of tiles in the bag. We should instead focus on deducing from the total number of tiles, which is 10.
Given that we have accounted for 24 blue tiles, 12 green tiles, and 12 red tiles in 100 pulls, we can also represent the proportions of the tiles. The counts of tiles should relate to how many of each color is in the bag.
To find how many yellow tiles are most likely in the bag, we need a reasonable distribution of the different colored tiles based on the proportion of colors represented in the pulls.
Let the number of yellow tiles be \( y \). We have:
\[ \text{Number of total tiles} = \text{Blue} + \text{Green} + \text{Red} + \text{Yellow} = 10 \]
Also, from the data of 100 pulls, we derive the proportions:
- Ratio of blue tiles pulled: \( \frac{24}{100} = 0.24 \)
- Ratio of green tiles pulled: \( \frac{12}{100} = 0.12 \)
- Ratio of red tiles pulled: \( \frac{12}{100} = 0.12 \)
Let’s denote:
- Number of blue tiles = \( b \)
- Number of green tiles = \( g \)
- Number of red tiles = \( r \)
- Number of yellow tiles = \( y \)
We can assume that the probabilities reflect the number of tiles in the bag. Since the proportions of the blue, green, and red tiles match closely to the total number of tiles represented, we can approximate by setting ratios:
\[ \frac{b}{10} \approx 0.24, \quad \frac{g}{10} \approx 0.12, \quad \frac{r}{10} \approx 0.12 \]
To find expected \( b, g, r \) we can observe:
Assuming the most balanced distribution of the remaining colors in the tiles fitting \( y + b + g + r = 10 \):
Let \( b = 2, g = 1, r = 1 \) thus resulting:
\[ 10 - (b + g + r) = y \]
Solving gives \( y = 10 - 4 = 6\).
After calculations, I conclude the most likely number of yellow tiles is:
Answer: 6