A bag contains five yellow balls and some white balls. If the probability of picking a white ball is twice that of picking a yellow ball, how many white balls are there?

Options

A. 20
B. 10
C. 16
D. 18

Answer

To solve the problem, we need to find the number of white balls in the bag, given that the probability of picking a white ball is twice that of picking a yellow ball.

### Step-by-step Solution:

1. **Identify the number of yellow balls**:
- We know there are 5 yellow balls in the bag.

2. **Let the number of white balls be \( w \)**:
- We will denote the number of white balls as \( w \).

3. **Calculate the total number of balls**:
- The total number of balls in the bag is the sum of yellow and white balls, which is \( 5 + w \).

4. **Determine the probability of picking a yellow ball**:
- The probability of picking a yellow ball is given by the formula:
\[ P(\text{Yellow}) = \frac{\text{Number of Yellow Balls}}{\text{Total Number of Balls}} = \frac{5}{5 + w} \]

5. **Determine the probability of picking a white ball**:
- The probability of picking a white ball is:
\[ P(\text{White}) = \frac{\text{Number of White Balls}}{\text{Total Number of Balls}} = \frac{w}{5 + w} \]

6. **Set up the equation based on the given condition**:
- According to the problem, the probability of picking a white ball is twice that of picking a yellow ball:
\[ P(\text{White}) = 2 \times P(\text{Yellow}) \]
- Substituting the probabilities we calculated:
\[ \frac{w}{5 + w} = 2 \times \frac{5}{5 + w} \]

7. **Solve the equation**:
- Cross-multiply to eliminate the fractions:
\[ w = 2 \times 5 \]
\[ w = 10 \]

8. **Conclusion**:
- Therefore, the number of white balls in the bag is \( 10 \).

### Final Answer:
The number of white balls is **10**.

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