To solve these questions, let's first analyze the given tabular data that represents the cards drawn from the bag.
### Representation of Cards:
```
Row 1: Green | White | Green
Row 2: Red | Black | White
Row 3: Black | White | Green
Row 4: Red | Red | Red
Row 5: White | Red |
```
From this, we can count the number of cards and the number of cards of each color (particularly focusing on white cards for this question).
### 2.1 Determine the Probability of Drawing a White Card:
- Total number of cards:
There are 14 cards in total.
- Number of white cards:
Let's count the white cards in each row:
- Row 1: 1 white card
- Row 2: 1 white card
- Row 3: 1 white card
- Row 5: 1 white card
Therefore, the total number of white cards is 4.
- Probability Calculation:
[tex]\[
\text{Probability of drawing a white card} = \frac{\text{Number of white cards}}{\text{Total number of cards}}
\][/tex]
[tex]\[
\text{Probability of drawing a white card} = \frac{4}{14} = \frac{2}{7} \approx 0.2857
\][/tex]
So, the simplified probability of drawing a white card is [tex]\(\frac{2}{7}\)[/tex].
### 2.2 Determine the Color of the Card with a Probability of 0.14:
Let's calculate the number of cards needed to have a probability of 0.14:
[tex]\[
\text{Probability (P)} = \frac{\text{Number of a specific color card}}{\text{Total number of cards}}
\][/tex]
Given [tex]\( P = 0.14 \)[/tex] and the total number of cards is 14,
[tex]\[
0.14 = \frac{\text{Number of a specific color card}}{14}
\][/tex]
Multiplying both sides by 14 to solve for the number of cards,
[tex]\[
0.14 \times 14 = \text{Number of a specific color card}
\][/tex]
[tex]\[
1.96 \][/tex]
Since the number of cards must be a whole number, we round to the nearest integer, which is 2. Hence, there should be 2 cards of a certain color to get a probability close to 0.14.
Now, let's match this with the given data to determine which colors have 2 cards:
- Green cards:
- Row 1: 2 green cards
- Row 3: 1 green card
Total: 3 green cards
- Red cards:
- Row 2: 1 red card
- Row 4: 3 red cards
- Row 5: 1 red card
Total: 5 red cards
- Black cards:
- Row 2: 1 black card
- Row 3: 1 black card
Total: 2 black cards
Thus, the color with exactly 2 cards and matching the probability closest to 0.14 is Black.
Therefore, the color of the card with a probability of 0.14 is Black.
